From bbba403f685f2256f8c9066267a1439548305aa2 Mon Sep 17 00:00:00 2001 From: smruthig <75429779+smruthig@users.noreply.github.com> Date: Mon, 12 Feb 2024 21:54:27 -0800 Subject: [PATCH] Added code files --- .../Global Binary Measures.ipynb | 1 + .../Global Weighted Measures.ipynb | 1 + .../Local Binary Measures.ipynb | 1 + .../Local Weighted Measures.ipynb | 1 + .../XGB for threshold comparison.ipynb | 1 + ...Data Augmentation Distribution sampling.ipynb | 1 + .../All ML Models 10 fold CV.ipynb | 1 + .../DGCNN model 10 Fold CV.ipynb | 1 + Code/5. Graph Neural Network/DGCNN model.ipynb | 1 + .../DGCNN with node2vec.ipynb | 1 + .../GCN model 10 fold CV.ipynb | 1 + .../RLF feature selection.ipynb | 1 + Code/6. Biomarker Detection/SpeCo.ipynb | 1 + Code/README.md.docx | Bin 0 -> 8702 bytes 14 files changed, 13 insertions(+) create mode 100644 Code/1. Feature Generation/Global Binary Measures.ipynb create mode 100644 Code/1. Feature Generation/Global Weighted Measures.ipynb create mode 100644 Code/1. Feature Generation/Local Binary Measures.ipynb create mode 100644 Code/1. Feature Generation/Local Weighted Measures.ipynb create mode 100644 Code/2. Threshold Comparison/XGB for threshold comparison.ipynb create mode 100644 Code/3. Data Augmentation/Data Augmentation Distribution sampling.ipynb create mode 100644 Code/4. Machine Learning/All ML Models 10 fold CV.ipynb create mode 100644 Code/5. Graph Neural Network/DGCNN model 10 Fold CV.ipynb create mode 100644 Code/5. Graph Neural Network/DGCNN model.ipynb create mode 100644 Code/5. Graph Neural Network/DGCNN with node2vec.ipynb create mode 100644 Code/5. Graph Neural Network/GCN model 10 fold CV.ipynb create mode 100644 Code/6. Biomarker Detection/RLF feature selection.ipynb create mode 100644 Code/6. Biomarker Detection/SpeCo.ipynb create mode 100644 Code/README.md.docx diff --git a/Code/1. Feature Generation/Global Binary Measures.ipynb b/Code/1. Feature Generation/Global Binary Measures.ipynb new file mode 100644 index 0000000..76e9d68 --- /dev/null +++ b/Code/1. Feature Generation/Global Binary Measures.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","metadata":{"id":"U7XnRxphhudt"},"source":["# IMPORT STATEMENTS"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true},"id":"OXjAAcZCdaPk"},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","import networkx as nx\n","import os\n","import matplotlib.pyplot as plt\n","import graphviz\n","from operator import itemgetter\n","from networkx.algorithms import approximation as approx\n","from networkx.algorithms import bipartite"]},{"cell_type":"markdown","metadata":{"id":"X7tW3FIbhzX2"},"source":["# DATA LOADING"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"p-8aq6oLe0wn"},"outputs":[],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"iO66ONDNSSYn"},"outputs":[],"source":["# Labels\n","combined_phenotype= '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","labels_mappings"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"hontMDXXfRB-"},"outputs":[],"source":["ub = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"euDWtNH76rjP"},"outputs":[],"source":["# Add the directories as per requirement\n","dirs = [ub]\n","\n","graphs = list()\n","labels = list()\n","\n","for dir in dirs:\n"," for file in os.listdir(dir):\n"," if file.endswith(\".csv\"):\n"," if (dir == ub):\n"," subject = file[12:16]\n"," elif (dir == uw):\n"," subject = file[14:18]\n"," else:\n"," print(\"If you are using a statically binarized folder:\")\n"," print(\"Add a condition along with cb condition for COBRE and ub condition for UCLA\")\n"," print(\"Example: elif (dir == ub) becomes elif (dir == ub) or (dir == ub0_3)\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," mask = labels_mappings['Subject'] == int(subject)\n"," labels.append((labels_mappings[mask]['Label'].values[0], int(subject)))\n","\n"," # APPENDING CORRESPONDING GRAPH - may change based on implementation\n"," df = pd.read_csv(dir+file, header=None)\n"," G = nx.from_pandas_adjacency(df)\n"," graphs.append(G) "]},{"cell_type":"markdown","metadata":{"id":"fPgrpAooqz_B"},"source":["# INDIVIDUAL SUBJECT EXPLORATION"]},{"cell_type":"markdown","metadata":{"id":"5SppRteFh3rc"},"source":["## Basic information about the graph"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"b1877Uy4fWwg"},"outputs":[],"source":["G = nx.from_pandas_adjacency(df)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"kXriVxTYfd4O"},"outputs":[],"source":["print(\"Number of nodes in the graph:\", len(G.nodes()))\n","print(\"Nodes:\", G.nodes())\n","print()\n","print(\"Number of edges in the graph:\", len(G.edges()))\n","print(\"Edges:\", G.edges(data=True))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"e3ssXGpBfhqH"},"outputs":[],"source":["plt.figure(3,figsize=(20,12)) \n","nx.draw(G, with_labels=True, node_size=700, font_size=8)\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"jkXTkpjEib0a"},"source":["## Global measures"]},{"cell_type":"markdown","metadata":{"id":"wVoCoCtG0Qn3"},"source":["### Chain decomposition"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"jnOHS4dhzkzX"},"outputs":[],"source":["ch = nx.chain_decomposition(G)\n","ch = list(ch)\n","ch"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"2jWadMn-5ZRs"},"outputs":[],"source":["reachable = {}\n","for l in ch:\n"," for t in l:\n"," s=t[0]\n"," d=t[1]\n"," if s not in reachable:\n"," reachable[s]=[d]\n"," else:\n"," reachable[s].append(d)\n","\n"," if d not in reachable:\n"," reachable[d]=[s]\n"," else:\n"," reachable[d].append(s)\n","\n","max_l = 0\n","highest = -1\n","for i in sorted (reachable) :\n"," print ((i, reachable[i]), end =\" \")\n"," if len(reachable[i])>max_l:\n"," max_l = len(reachable[i])\n"," highest = i\n"," print()\n","\n","print(\"Most connected node: \", highest, \" connected to \", max_l,\" nodes\")"]},{"cell_type":"markdown","metadata":{"id":"9IQSFgfi3lcv"},"source":["# Utility function (for measures' calculations)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"FOV_iP2L3nh9"},"outputs":[],"source":["class global_measures_binary:\n","\n"," def __init__(self, subject_no, schiz, G, df):\n"," self.G = G\n"," self.subject = subject_no\n"," if schiz:\n"," self.schiz = 'Schizophrenic'\n"," else:\n"," self.schiz = 'Control'\n"," self.df = df\n"," self.df.at[self.subject, \"Subject\"] = self.subject\n"," self.df.at[self.subject, \"Schizophrenic\"] = int(schiz)\n"," \n"," print('\\n\\nSUBJECT NUMBER: ',self.subject)\n"," \n"," self.approx_node_connectivity()\n"," self.approx_max_independent_sets()\n"," self.approx_max_clique()\n"," self.approx_clique_removal()\n"," self.approx_large_clique_size()\n"," self.approx_avg_clustering()\n"," self.approx_diameter()\n"," self.approx_min_edge_dominating_set()\n"," self.approx_min_wt_dominatind_set()\n"," self.approx_maximal_matching()\n"," self.approx_ramsay()\n"," self.approx_tsp()\n"," self.approx_treewidth_min_degree()\n"," self.approx_treewidth_min_fill_in()\n"," self.approx_min_wt_vertex_cover()\n"," self.approx_randomised_partitioning()\n"," self.approx_one_exchange()\n"," self.assortativity()\n"," self.avg_shortest_path_length()\n"," self.asteroidal_triplet()\n"," self.bridges()\n"," self.local_bridges()\n"," self.colouring()\n"," self.avg_degree()\n"," self.global_clustering()\n"," self.edges()\n"," self.chordal()\n"," self.cliques()\n"," self.num_of_isolates()\n"," self.non_randomness()\n"," self.transitivity()\n"," self.connected_components()\n"," self.diameter()\n"," self.k_edge_connected(1)\n"," self.k_edge_connected(2)\n"," self.k_edge_connected(3)\n","\n"," def approx_node_connectivity(self):\n"," print(\"Approximation and Heuristics Node Connectivity\")\n"," r = approx.node_connectivity(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Node Connectivity\"] = r\n","\n"," def approx_k_components(self):\n"," print(\"Approximation and Heuristics K Components\")\n"," r = approx.k_components(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics K Components\"] = r\n","\n"," def approx_max_independent_sets(self):\n"," print(\"Approximation and Heuristics Max Independent Sets\")\n"," r = approx.maximum_independent_set(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Max Independent Sets\"] = str(r)\n","\n"," def approx_max_clique(self):\n"," print(\"Approximation and Heuristics Max Cliques\")\n"," r = approx.max_clique(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Max Cliques\"] = str(r)\n","\n"," def approx_clique_removal(self):\n"," print(\"Approximation and Heuristics Clique Removal\")\n"," r = approx.clique_removal(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Clique Removal\"] = str(r)\n","\n"," def approx_large_clique_size(self):\n"," print(\"Approximation and Heuristics Large Clique Size\")\n"," r = approx.large_clique_size(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Large Clique Size\"] = r\n","\n"," def approx_avg_clustering(self):\n"," print(\"Approximation and Heuristics Average Clustering\")\n"," r = approx.average_clustering(self.G, trials=1000, seed=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics Average Clustering\"] = r\n","\n"," def approx_diameter(self):\n"," print(\"Approximation and Heuristics Diameter\")\n"," r = approx.diameter(self.G, seed=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics Diameter\"] = r\n","\n"," def approx_min_edge_dominating_set(self):\n"," print(\"Approximation and Heuristics Min Edge Dominating Set\")\n"," r = approx.min_edge_dominating_set(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Min Edge Dominating Set\"] = str(r)\n","\n"," def approx_min_wt_dominatind_set(self):\n"," print(\"Approximation and Heuristics Min Wt Dominating Set\")\n"," r = approx.min_weighted_dominating_set(self.G, weight=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics Min Wt Dominating Set\"] = str(r)\n","\n"," def approx_maximal_matching(self):\n"," print(\"Approximation and Heuristics Maximal Matching\")\n"," r = nx.maximal_matching(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Maximal Matching\"] = str(r)\n","\n"," def approx_ramsay(self):\n"," print(\"Approximation and Heuristics Ramsay\")\n"," r = approx.ramsey_R2(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics Ramsay\"] = str(r)\n","\n"," def approx_tsp(self):\n"," print(\"Approximation and Heuristics TSP\")\n"," r = approx.traveling_salesman_problem(self.G, weight='weight', nodes=None, cycle=True, method=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics TSP\"] = str(r)\n"," \n"," def approx_treewidth_min_degree(self):\n"," print(\"Approximation and Heuristics treewidth Min Degree\")\n"," r = approx.treewidth_min_degree(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics treewidth Min Degree\"] = r[0]\n","\n"," def approx_treewidth_min_fill_in(self):\n"," print(\"Approximation and Heuristics treewidth Min Fill In\")\n"," r = approx.treewidth_min_degree(self.G)\n"," self.df.at[self.subject, \"Approximation and Heuristics treewidth Min Fill In\"] = r[0]\n","\n"," def approx_min_wt_vertex_cover(self):\n"," print(\"Approximation and Heuristics treewidth Min Wt Vertex Cover\")\n"," r = approx.min_weighted_vertex_cover(self.G, weight=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics treewidth Min Wt Vertex Cover\"] = str(r)\n","\n"," def approx_randomised_partitioning(self):\n"," print(\"Approximation and Heuristics Randomized Partitioning\")\n"," r = approx.randomized_partitioning(self.G, seed=None, p=0.5, weight=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics Randomized Partitioning\"] = str(r)\n","\n"," def approx_one_exchange(self):\n"," print(\"Approximation and Heuristics One Exchange\")\n"," r = approx.one_exchange(self.G, initial_cut=None, seed=None, weight=None)\n"," self.df.at[self.subject, \"Approximation and Heuristics One Exchange\"] = str(r)\n","\n"," def assortativity(self):\n"," print(\"Degree Assortativity\")\n"," r = nx.degree_assortativity_coefficient(self.G)\n"," self.df.at[self.subject, \"Degree Assortativity\"] = r\n","\n"," def avg_shortest_path_length(self):\n"," print(\"Avg Shortest Path Length\")\n"," if nx.number_connected_components(self.G) is 1:\n"," r = nx.average_shortest_path_length(self.G)\n"," self.df.at[self.subject, \"Avg Shortest Path Length\"] = r\n"," else:\n"," self.df.at[self.subject, \"Avg Shortest Path Length\"] = np.NaN\n","\n"," def asteroidal_triplet(self):\n"," print(\"Asteroidal Triple\")\n"," if not nx.is_at_free(self.G):\n"," r = nx.find_asteroidal_triple(self.G)\n"," else:\n"," r = []\n"," self.df.at[self.subject, \"Asteroidal Triple\"] = str(r)\n","\n"," def is_bipartite(self):\n"," print(\"Is Bipartite\")\n"," r = nx.is_bipartite(self.G)\n"," self.df.at[self.subject, \"Is Bipartite\"] = r\n","\n"," def bipartite_color(self):\n"," print(\"Bipartite Color\")\n"," r = bipartite.color(self.G)\n"," self.df.at[self.subject, \"Bipartite Color\"] = str(r)\n","\n"," def bridges(self):\n"," print(\"Bridges\")\n"," r = nx.has_bridges(self.G)\n"," self.df.at[self.subject, \"Bridges\"] = r\n","\n"," def print_bridges(self):\n"," r = nx.has_bridges(self.G)\n"," if r:\n"," print(self.subject,\"->\",self.schiz,\"-> has bridges: \", list(nx.bridges(self.G)))\n","\n"," def local_bridges(self):\n"," print(\"Local bridges\")\n"," r = len(set(nx.local_bridges(self.G)))\n"," self.df.at[self.subject, \"Local Bridges\"] = r\n","\n"," def colouring(self):\n"," print(\"Graph coloring\")\n"," r = nx.greedy_color(self.G)\n"," self.df.at[self.subject, \"Graph colouring\"] = max(r.values())\n","\n"," def avg_degree(self):\n"," print(\"Avg Degree\")\n"," N,K = self.G.order(), self.G.size()\n"," self.df.at[self.subject, \"Avg Degree\"] = float(K)/N\n","\n"," def global_clustering(self):\n"," print(\"Global Clustering\")\n"," r = nx.average_clustering(self.G)\n"," self.df.at[self.subject, \"Global Clustering\"] = r\n","\n"," def edges(self):\n"," print(\"Edges\")\n"," r = len(self.G.edges())\n"," self.df.at[self.subject, \"Edges\"] = r\n","\n"," def chordal(self):\n"," print(\"Chordal\")\n"," r = nx.is_chordal(self.G)\n"," self.df.at[self.subject, \"Chordal\"] = r\n","\n"," # maximal cliques\n"," def cliques(self):\n"," print(\"Maximal Cliques\")\n"," r = nx.graph_number_of_cliques(self.G)\n"," self.df.at[self.subject, \"Maximal Cliques\"] = r\n"," \n"," # maximal cliques\n"," def print_cliques(self):\n"," r = list(nx.find_cliques(self.G))\n"," print(self.subject,\"->\",self.schiz,\"-> has cliques: \", r)\n","\n"," def num_of_isolates(self):\n"," print(\"Num of isolates\")\n"," r = nx.number_of_isolates(self.G)\n"," self.df.at[self.subject, \"Num of isolates\"] = r\n","\n"," def non_randomness(self):\n"," print(\"Non Randomness wrt Random Model\")\n"," if nx.number_connected_components(self.G) is 1:\n"," nr, nr_rd = nx.non_randomness(self.G)\n"," self.df.at[self.subject, \"Non Randomness wrt Random Model\"] = nr_rd\n"," else:\n"," self.df.at[self.subject, \"Non Randomness wrt Random Model\"] = np.NaN\n","\n"," def print_chain_decomposition(self):\n"," r = list(nx.chain_decomposition(self.G))\n"," print(self.subject,\"->\",self.schiz,\"-> has chain: \", r)\n","\n"," def transitivity(self):\n"," print(\"Transitivity\")\n"," r = nx.transitivity(self.G)\n"," self.df.at[self.subject, \"Transitivity\"] = r\n","\n"," def connected_components(self):\n"," print(\"Connected Components\")\n"," r = nx.number_connected_components(self.G)\n"," self.df.at[self.subject, \"Connected Components\"] = r\n","\n"," def k_edge_connected(self, k):\n"," print(str(k)+\" Edge Connected\")\n"," r = nx.is_k_edge_connected(self.G, k=k)\n"," self.df.at[self.subject, str(k)+\" Edge Connected\"] = r\n","\n"," def diameter(self):\n"," print(\"Diameter\")\n"," r = nx.diameter(self.G)\n"," self.df.at[self.subject, \"Diameter\"] = r"]},{"cell_type":"markdown","metadata":{"id":"HQcrtNqdrVqf"},"source":["# Driver function"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true,"base_uri":"https://localhost:8080/"},"id":"xoHE9ilerSHt","outputId":"2ed5f445-f861-4ff1-dd65-44e48caf06bc"},"outputs":[{"name":"stdout","output_type":"stream","text":["\u001b[1;30;43mStreaming output truncated to the last 5000 lines.\u001b[0m\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2048\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2073\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2076\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2039\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2051\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2049\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2075\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2043\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2069\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2027\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2074\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2058\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2055\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2065\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2053\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2046\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2072\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2034\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2041\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2057\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2031\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2066\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2064\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2032\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2054\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2071\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2060\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2028\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2045\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2050\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2047\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2037\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2099\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2114\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2108\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2104\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2078\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2101\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2110\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2081\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2087\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2121\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2092\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2079\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2080\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2113\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2094\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2112\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2091\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2090\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2105\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2102\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2088\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2109\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2084\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2098\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2118\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2119\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2115\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2086\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2124\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2100\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2117\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2103\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2125\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2085\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2120\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2097\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2089\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2107\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2106\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2095\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2093\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2083\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2122\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2111\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2082\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2126\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2116\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2096\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2077\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2123\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2148\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2155\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2130\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2171\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2129\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2151\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2145\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2142\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2156\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2143\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2167\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2144\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2147\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2152\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2163\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2138\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2159\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2158\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2134\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2169\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2136\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2137\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2166\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2170\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2128\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2149\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2172\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2168\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2160\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2154\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2161\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2140\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2164\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2165\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2146\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2150\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2141\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2131\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2135\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2127\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2132\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2162\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2157\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected Components\n","Diameter\n","1 Edge Connected\n","2 Edge Connected\n","3 Edge Connected\n","\n","\n","SUBJECT NUMBER: 2139\n","Approximation and Heuristics Node Connectivity\n","Approximation and Heuristics Max Independent Sets\n","Approximation and Heuristics Max Cliques\n","Approximation and Heuristics Clique Removal\n","Approximation and Heuristics Large Clique Size\n","Approximation and Heuristics Average Clustering\n","Approximation and Heuristics Diameter\n","Approximation and Heuristics Min Edge Dominating Set\n","Approximation and Heuristics Min Wt Dominating Set\n","Approximation and Heuristics Maximal Matching\n","Approximation and Heuristics Ramsay\n","Approximation and Heuristics TSP\n","Approximation and Heuristics treewidth Min Degree\n","Approximation and Heuristics treewidth Min Fill In\n","Approximation and Heuristics treewidth Min Wt Vertex Cover\n","Approximation and Heuristics Randomized Partitioning\n","Approximation and Heuristics One Exchange\n","Degree Assortativity\n","Avg Shortest Path Length\n","Asteroidal Triple\n","Bridges\n","Local bridges\n","Graph coloring\n","Avg Degree\n","Global Clustering\n","Edges\n","Chordal\n","Maximal Cliques\n","Num of isolates\n","Non Randomness wrt Random Model\n","Transitivity\n","Connected 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SubjectSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating SetApproximation and Heuristics Min Wt Dominating SetApproximation and Heuristics Maximal MatchingApproximation and Heuristics RamsayApproximation and Heuristics TSPApproximation and Heuristics treewidth Min DegreeApproximation and Heuristics treewidth Min Fill InApproximation and Heuristics treewidth Min Wt Vertex CoverApproximation and Heuristics Randomized PartitioningApproximation and Heuristics One ExchangeDegree AssortativityAvg Shortest Path LengthAsteroidal TripleBridgesLocal BridgesGraph colouringAvg DegreeGlobal ClusteringEdgesChordalMaximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge Connected
20192019.00.043.0{128, 0, 4, 147, 89, 156}{11, 13, 14, 15, 16, 17, 21, 22, 23, 26, 27, 2...({128, 0, 4, 147, 89, 156}, [{4, 133, 6, 5, 16...39.00.6932.0{(54, 55), (100, 101), (40, 41), (72, 73), (18...{2, 136, 14, 16, 20, 21, 22, 26, 27, 28, 29, 3...{(54, 55), (100, 101), (40, 41), (72, 73), (18...({4, 133, 6, 5, 16, 21, 44, 45, 50, 51, 57, 59...[0, 160, 0, 86, 81, 1, 159, 1, 99, 69, 82, 85,...127.0127.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3769, ({0, 1, 2, 3, 4, 5, 7, 9, 12, 14, 17, 1...(4076, ({0, 1, 2, 6, 11, 14, 15, 16, 17, 20, 2...0.3208751.437977[104, 115, 128]False0.049.045.8048780.6883337512.0False227045.00.07.2772490.6983361.02.0TrueTrueTrue
20242024.00.062.0{33, 4, 134, 8, 12, 56}{5, 6, 7, 10, 145, 44, 45, 46, 47, 48, 51, 52,...({33, 4, 134, 8, 12, 56}, [{0, 1, 2, 131, 3, 6...31.00.6442.0{(54, 55), (86, 87), (100, 101), (154, 156), (...{96, 98, 101, 102, 133, 139, 144, 117, 91, 62,...{(54, 55), (86, 87), (100, 101), (154, 156), (...({0, 1, 2, 131, 3, 6, 18, 25, 29, 32, 49, 53, ...[0, 161, 4, 130, 41, 7, 92, 73, 1, 108, 56, 15...144.0144.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3699, ({2, 3, 6, 7, 9, 14, 20, 21, 22, 23, 24...(4000, ({1, 2, 3, 5, 6, 11, 12, 13, 14, 15, 16...0.1738361.448825[80, 125, 134]False0.043.044.9207320.6436017367.0False165809.00.02.4959790.6445651.02.0TrueTrueTrue
20222022.00.042.0{1, 100, 5, 36, 159}{0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 32...({1, 100, 5, 36, 159}, [{0, 1, 2, 131, 4, 133,...32.00.6592.0{(54, 55), (86, 87), (154, 156), (40, 41), (72...{3, 131, 135, 136, 144, 24, 32, 33, 38, 45, 46...{(54, 55), (86, 87), (154, 156), (40, 41), (72...({0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 3...[0, 161, 162, 1, 79, 4, 82, 81, 150, 12, 6, 10...140.0140.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3750, ({8, 10, 12, 13, 14, 16, 19, 22, 25, 26...(4069, ({0, 3, 4, 8, 10, 13, 14, 15, 17, 18, 1...0.1585011.438875[39, 70, 131]False0.042.045.7317070.6683387500.0False261112.00.03.8936000.6665961.02.0TrueTrueTrue
20152015.00.060.0{128, 0, 76, 148, 29}{6, 7, 8, 9, 10, 145, 146, 147, 21, 150, 157, ...({128, 0, 76, 148, 29}, [{128, 129, 134, 12, 1...30.00.6492.0{(54, 55), (86, 87), (100, 101), (125, 126), (...{32, 162, 163, 100, 145, 149, 150, 151, 152, 5...{(54, 55), (86, 87), (100, 101), (125, 126), (...({128, 129, 134, 12, 13, 14, 15, 16, 17, 22, 1...[0, 163, 0, 158, 1, 107, 61, 1, 108, 54, 1, 12...131.0131.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3400, ({0, 1, 2, 3, 4, 6, 10, 12, 14, 16, 17,...(3712, ({0, 1, 4, 5, 6, 11, 12, 13, 14, 15, 19...0.0915871.497755[29, 44, 0]False0.044.040.9329270.6585756713.0False33730.00.00.7661250.6528571.02.0TrueTrueTrue
20252025.00.050.0{130, 100, 5, 6, 9, 154}{129, 8, 141, 19, 22, 23, 28, 29, 31, 32, 33, ...({130, 100, 5, 6, 9, 154}, [{0, 1, 2, 3, 4, 14...26.00.6392.0{(54, 55), (86, 87), (92, 93), (156, 157), (40...{99, 4, 41, 137, 43, 44, 14, 47, 22, 152}{(54, 55), (86, 87), (92, 93), (156, 157), (40...({0, 1, 2, 3, 4, 14, 18, 19, 29, 32, 33, 36, 3...[0, 157, 2, 66, 101, 95, 69, 4, 82, 85, 84, 83...142.0142.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3768, ({1, 2, 4, 5, 6, 8, 10, 11, 14, 15, 16,...(4032, ({1, 4, 8, 9, 10, 12, 13, 14, 18, 21, 2...0.0944961.441568[100, 112, 0]False0.042.045.5121950.6435467464.0False289857.00.02.7065200.6407871.02.0TrueTrueTrue
20172017.00.035.0{32, 101, 137, 12, 151, 125}{6, 8, 9, 10, 17, 146, 147, 20, 21, 19, 18, 30...({32, 101, 137, 12, 151, 125}, [{4, 5, 6, 9, 1...29.00.6522.0{(54, 55), (100, 101), (125, 126), (154, 156),...{4, 146, 147, 150, 27, 30, 161, 162, 163, 35, ...{(54, 55), (100, 101), (125, 126), (154, 156),...({4, 5, 6, 9, 10, 18, 147, 20, 21, 30, 159, 34...[0, 163, 0, 99, 68, 4, 76, 92, 85, 84, 91, 72,...146.0146.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3902, ({1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 14, ...(4188, ({2, 3, 4, 6, 12, 13, 14, 16, 22, 24, 2...0.1428651.416130[20, 162, 128]False0.045.047.5853660.6719617804.0False465583.00.03.6867760.6724501.02.0TrueTrueTrue
20102010.00.042.0{66, 130, 4, 106, 75, 124}{12, 13, 14, 15, 16, 17, 25, 26, 28, 29, 36, 3...({66, 130, 4, 106, 75, 124}, [{0, 1, 2, 3, 22,...32.00.6752.0{(54, 55), (86, 87), (125, 126), (156, 157), (...{130, 4, 5, 11, 12, 140, 143, 16, 145, 157, 16...{(54, 55), (86, 87), (125, 126), (156, 157), (...({0, 1, 2, 3, 22, 23, 25, 27, 32, 33, 38, 39, ...[0, 120, 0, 163, 84, 85, 83, 86, 82, 0, 87, 81...137.0137.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3664, ({0, 1, 3, 5, 6, 8, 9, 10, 12, 14, 17, ...(4001, ({0, 1, 2, 4, 5, 6, 8, 9, 10, 11, 12, 1...0.2180991.447329[39, 70, 131]False0.045.045.0426830.6603527387.0False340624.00.05.6745850.6641321.02.0TrueTrueTrue
20202020.00.047.0{129, 4, 102, 11, 87, 121}{130, 11, 13, 15, 16, 17, 151, 27, 29, 32, 34,...({129, 4, 102, 11, 87, 121}, [{0, 1, 2, 3, 148...29.00.6512.0{(54, 55), (86, 87), (92, 93), (40, 41), (72, ...{130, 37, 103, 43, 148, 149, 150, 151}{(54, 55), (86, 87), (92, 93), (40, 41), (72, ...({0, 1, 2, 3, 148, 149, 23, 28, 29, 47, 53, 54...[0, 86, 85, 87, 84, 88, 83, 93, 79, 98, 74, 97...144.0144.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3646, ({1, 3, 4, 7, 9, 10, 11, 12, 15, 16, 18...(3962, ({18, 21, 22, 24, 26, 27, 28, 29, 30, 3...0.1566591.446207[39, 70, 0]False0.040.045.1341460.6449297402.0False433172.00.03.6327260.6456521.02.0TrueTrueTrue
20262026.00.051.0{0, 4, 38, 144, 19, 58}{2, 8, 140, 141, 148, 149, 22, 23, 24, 26, 27,...({0, 4, 38, 144, 19, 58}, [{128, 4, 5, 6, 12, ...23.00.6082.0{(54, 55), (86, 87), (156, 157), (40, 41), (72...{101, 137, 114, 148, 151, 157, 30}{(54, 55), (86, 87), (156, 157), (40, 41), (72...({128, 4, 5, 6, 12, 13, 16, 34, 35, 45, 48, 49...[0, 158, 3, 64, 115, 1, 160, 104, 63, 2, 137, ...138.0138.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3564, ({1, 2, 3, 5, 7, 9, 12, 13, 18, 21, 23,...(3799, ({0, 2, 5, 6, 9, 10, 12, 13, 14, 15, 18...0.0732581.471644[20, 162, 1]False0.041.043.0609760.6226047062.0False140155.00.01.7908430.6186051.02.0TrueTrueTrue
20232023.00.058.0{128, 68, 15, 145, 83, 28}{7, 9, 10, 13, 15, 17, 21, 152, 35, 42, 66, 74...({128, 68, 15, 145, 83, 28}, [{160, 129, 66, 1...26.00.6202.0{(54, 55), (86, 87), (92, 93), (156, 157), (72...{34, 35, 36, 11, 76, 12, 111, 115, 84, 116, 86...{(54, 55), (86, 87), (92, 93), (156, 157), (72...({160, 129, 66, 130, 70, 7, 9, 74, 10, 140, 77...[0, 163, 162, 1, 145, 24, 7, 140, 31, 57, 121,...146.0146.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3582, ({0, 1, 5, 7, 8, 10, 11, 16, 17, 18, 20...(3886, ({0, 1, 2, 3, 5, 6, 11, 12, 13, 14, 17,...0.1284231.467006[39, 70, 0]False0.038.043.4390240.6218437124.0False170074.00.01.9534700.6213981.02.0TrueTrueTrue
20012001.00.052.0{0, 162, 99, 130, 47, 56}{10, 148, 149, 22, 151, 24, 25, 26, 27, 28, 29...({0, 162, 99, 130, 47, 56}, [{96, 65, 1, 0, 6,...25.00.6272.0{(54, 55), (86, 87), (100, 101), (156, 157), (...{106, 44, 46, 48, 146, 50, 51, 85, 60, 30}{(54, 55), (86, 87), (100, 101), (156, 157), (...({96, 65, 1, 0, 6, 111, 144, 145, 50, 83, 49, ...[0, 161, 158, 3, 69, 104, 87, 84, 88, 83, 91, ...129.0129.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3443, ({1, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20,...(3721, ({0, 6, 11, 13, 15, 18, 20, 22, 23, 26,...0.0770161.488104[39, 70, 97]False0.040.041.7195120.6240676842.0False95316.00.01.2952600.6197081.02.0TrueTrueTrue
20182018.00.048.0{0, 1, 163, 69, 139, 26}{1, 2, 131, 4, 5, 6, 10, 144, 146, 19, 18, 21,...({0, 1, 163, 69, 139, 26}, [{1, 2, 131, 4, 5, ...37.00.6502.0{(54, 55), (86, 87), (156, 157), (72, 73), (34...{96, 132, 101, 133, 134, 102, 137, 42, 144, 49...{(54, 55), (86, 87), (156, 157), (72, 73), (34...({1, 2, 131, 4, 5, 6, 10, 144, 146, 19, 18, 21...[0, 126, 42, 2, 61, 108, 85, 84, 87, 83, 0, 88...140.0140.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3586, ({0, 1, 2, 4, 9, 10, 12, 13, 14, 16, 18...(3821, ({1, 9, 14, 15, 17, 18, 19, 21, 22, 24,...0.2340871.468727[100, 112, 129]False0.045.043.2987800.6494417101.0False85479.00.03.7492770.6532831.02.0TrueTrueTrue
20072007.00.053.0{128, 3, 7, 136, 145, 86}{4, 5, 6, 9, 10, 13, 15, 16, 17, 21, 150, 28, ...({128, 3, 7, 136, 145, 86}, [{0, 1, 2, 4, 5, 6...32.00.6232.0{(54, 55), (86, 87), (92, 93), (125, 126), (15...{37, 9, 10, 46, 48, 50, 51, 116, 56, 62}{(54, 55), (86, 87), (92, 93), (125, 126), (15...({0, 1, 2, 4, 5, 6, 19, 153, 46, 48, 52, 61, 6...[0, 163, 156, 2, 68, 93, 96, 75, 1, 88, 86, 85...144.0144.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3645, ({2, 4, 5, 6, 7, 8, 10, 11, 13, 21, 22,...(3952, ({0, 1, 2, 8, 9, 15, 16, 18, 20, 21, 23...0.1469791.454137[20, 162, 2]False0.043.044.4878050.6487957296.0False127133.00.03.0199810.6482621.02.0TrueTrueTrue
20022002.00.050.0{0, 4, 138, 52, 93}{4, 5, 6, 7, 12, 13, 145, 147, 21, 150, 161, 3...({0, 4, 138, 52, 93}, [{4, 5, 6, 7, 12, 13, 14...44.00.6942.0{(54, 55), (86, 87), (100, 101), (156, 157), (...{96, 130, 132, 101, 102, 70, 133, 107, 13, 46,...{(54, 55), (86, 87), (100, 101), (156, 157), (...({4, 5, 6, 7, 12, 13, 145, 147, 21, 150, 161, ...[0, 160, 0, 99, 68, 1, 163, 94, 73, 74, 97, 4,...139.0139.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3926, ({0, 1, 2, 5, 6, 8, 10, 12, 13, 14, 15,...(4266, ({2, 3, 4, 5, 6, 7, 10, 14, 15, 17, 18,...0.1366001.411492[20, 162, 0]False0.051.047.9634150.6903877866.0False316538.00.04.4752540.6887481.02.0TrueTrueTrue
20092009.00.041.0{128, 0, 69, 137, 140}{9, 10, 12, 13, 15, 16, 20, 21, 26, 27, 29, 35...({128, 0, 69, 137, 140}, [{0, 1, 2, 3, 11, 22,...37.00.6752.0{(54, 55), (86, 87), (92, 93), (100, 101), (15...{97, 100, 102, 70, 104, 9, 40, 75, 106, 42, 13...{(54, 55), (86, 87), (92, 93), (100, 101), (15...({0, 1, 2, 3, 11, 22, 29, 32, 33, 36, 37, 38, ...[0, 85, 83, 87, 80, 93, 79, 88, 77, 89, 76, 90...139.0139.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3810, ({0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...(4082, ({1, 2, 4, 5, 9, 10, 19, 22, 27, 28, 29...0.2029401.437304[20, 162, 0]False0.046.045.8597560.6760307521.0False118837.00.04.5192130.6779791.02.0TrueTrueTrue
20162016.00.053.0{128, 1, 0, 5, 78, 112}{11, 12, 13, 14, 15, 18, 19, 20, 21, 32, 33, 3...({128, 1, 0, 5, 78, 112}, [{128, 130, 135, 136...25.00.6282.0{(54, 55), (86, 87), (156, 157), (40, 41), (72...{131, 36, 133, 123, 108, 91, 124}{(54, 55), (86, 87), (156, 157), (40, 41), (72...({128, 130, 135, 136, 12, 13, 14, 15, 33, 34, ...[0, 88, 87, 84, 83, 85, 82, 86, 81, 92, 80, 0,...137.0137.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3581, ({128, 2, 3, 4, 131, 134, 8, 9, 10, 11,...(3889, ({2, 5, 6, 7, 8, 10, 14, 17, 18, 19, 20...0.0926181.464761[20, 162, 10]False0.041.043.6219510.6447397154.0False132992.00.02.3864530.6411661.02.0TrueTrueTrue
20062006.00.063.0{67, 163, 135, 14, 57, 158}{138, 139, 12, 13, 15, 17, 146, 147, 20, 19, 1...({67, 163, 135, 14, 57, 158}, [{0, 1, 2, 131, ...38.00.6822.0{(6, 9), (54, 55), (86, 87), (92, 93), (100, 1...{152, 24, 117, 151}{(6, 9), (54, 55), (86, 87), (92, 93), (100, 1...({0, 1, 2, 131, 132, 133, 3, 152, 156, 157, 32...[0, 161, 157, 3, 111, 63, 1, 64, 103, 4, 114, ...148.0148.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(4208, ({1, 4, 5, 7, 8, 10, 11, 13, 14, 15, 19...(4420, ({2, 3, 4, 5, 10, 11, 18, 20, 21, 22, 2...0.0728661.380892[63, 76, 0]False0.048.050.4573170.7026558275.0False514570.00.03.7197360.6985301.02.0TrueTrueTrue
20032003.00.044.0{128, 131, 6, 24, 154, 156}{128, 130, 133, 134, 135, 11, 12, 13, 27, 32, ...({128, 131, 6, 24, 154, 156}, [{1, 2, 3, 5, 7,...28.00.6542.0{(14, 17), (54, 55), (86, 87), (156, 157), (40...{129, 46, 110, 49, 50, 51, 147, 54, 56, 28, 30...{(14, 17), (54, 55), (86, 87), (156, 157), (40...({1, 2, 3, 5, 7, 10, 144, 145, 19, 21, 155, 44...[0, 128, 43, 4, 114, 58, 46, 126, 85, 84, 86, ...144.0144.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3884, ({1, 3, 6, 7, 9, 10, 11, 12, 16, 17, 19...(4124, ({0, 1, 9, 10, 13, 16, 22, 27, 29, 30, ...0.1076291.425557[80, 125, 1]False0.044.046.8170730.6677627678.0False632171.00.04.0714280.6654431.02.0TrueTrueTrue
20082008.00.045.0{106, 123, 78, 15, 58, 27}{4, 5, 135, 136, 11, 12, 13, 16, 145, 18, 19, ...({106, 123, 78, 15, 58, 27}, [{0, 1, 2, 8, 19,...37.00.6972.0{(6, 9), (54, 55), (86, 87), (92, 93), (100, 1...{100, 136, 43, 108, 80, 144, 85, 152, 26, 92, ...{(6, 9), (54, 55), (86, 87), (92, 93), (100, 1...({0, 1, 2, 8, 19, 23, 25, 26, 29, 32, 33, 36, ...[0, 162, 1, 70, 100, 96, 69, 1, 101, 62, 78, 9...142.0142.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3947, ({0, 1, 3, 131, 134, 135, 8, 9, 137, 11...(4286, ({0, 3, 16, 17, 18, 19, 20, 21, 26, 27,...0.1433861.411492[63, 76, 129]False0.052.047.9634150.6882017866.0False430027.00.04.4570340.6870601.02.0TrueTrueTrue
20142014.00.058.0{0, 129, 1, 4, 119}{5, 6, 11, 12, 13, 14, 18, 34, 35, 43, 45, 65,...({0, 129, 1, 4, 119}, [{0, 2, 3, 7, 22, 23, 26...37.00.6672.0{(54, 55), (86, 87), (7, 12), (156, 157), (17,...{134, 135, 138, 46, 47}{(54, 55), (86, 87), (7, 12), (156, 157), (17,...({0, 2, 3, 7, 22, 23, 26, 28, 33, 162, 36, 41,...[0, 158, 122, 42, 2, 159, 1, 163, 97, 69, 107,...136.0136.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3721, ({0, 128, 130, 4, 133, 134, 7, 8, 135, ...(4006, ({2, 5, 7, 8, 11, 15, 16, 17, 18, 19, 2...0.1159361.446431[20, 162, 64]False0.044.045.1158540.6666037399.0False209043.00.02.7420110.6607471.02.0TrueTrueTrue
20212021.00.063.0{163, 9, 11, 19, 116, 126}{0, 132, 133, 134, 135, 8, 7, 6, 5, 4, 143, 14...({163, 9, 11, 19, 116, 126}, [{0, 132, 133, 13...24.00.6452.0{(54, 55), (86, 87), (100, 101), (125, 126), (...{135, 105, 10, 138, 107, 77, 46, 81, 59, 29, 31}{(54, 55), (86, 87), (100, 101), (125, 126), (...({0, 132, 133, 134, 135, 8, 7, 6, 5, 4, 143, 1...[0, 163, 162, 4, 129, 34, 6, 91, 67, 1, 100, 7...135.0135.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3423, ({0, 1, 5, 8, 9, 10, 14, 15, 16, 17, 18...(3692, ({0, 2, 4, 5, 6, 9, 10, 11, 12, 13, 14,...0.0617711.496110[20, 162, 2]False0.038.041.0670730.6170406735.0False59676.00.00.6961420.6141491.02.0TrueTrueTrue
20042004.00.051.0{4, 8, 75, 44, 13, 95}{1, 2, 3, 6, 17, 27, 28, 29, 40, 46, 48, 50, 5...({4, 8, 75, 44, 13, 95}, [{0, 1, 2, 3, 6, 17, ...27.00.6232.0{(6, 9), (65, 67), (54, 55), (82, 86), (156, 1...{70, 71, 40, 73, 47, 144, 113, 83, 27, 28, 157...{(6, 9), (65, 67), (54, 55), (82, 86), (156, 1...({0, 1, 2, 3, 6, 17, 27, 28, 29, 50, 51, 53, 5...[0, 158, 85, 83, 0, 84, 159, 4, 81, 87, 80, 0,...147.0147.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3729, ({0, 1, 3, 4, 9, 12, 13, 15, 16, 18, 23...(3943, ({0, 1, 4, 5, 7, 8, 16, 18, 21, 22, 26,...0.1483961.452491[39, 70, 130]False0.043.044.6219510.6388187318.0False221252.00.03.7304990.6403091.02.0TrueTrueTrue
20112011.00.051.0{65, 38, 7, 136, 11, 77}{132, 5, 134, 11, 12, 13, 16, 18, 34, 35, 42, ...({65, 38, 7, 136, 11, 77}, [{128, 1, 2, 3, 0, ...31.00.6602.0{(54, 55), (86, 87), (100, 101), (156, 157), (...{161, 17, 148, 154, 95}{(54, 55), (86, 87), (100, 101), (156, 157), (...({128, 1, 2, 3, 0, 71, 73, 75, 140, 17, 148, 5...[0, 162, 1, 94, 77, 96, 72, 103, 70, 1, 102, 6...140.0140.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3814, ({0, 4, 5, 6, 8, 11, 15, 19, 20, 21, 22...(4106, ({0, 1, 4, 5, 6, 9, 10, 12, 14, 15, 17,...0.1117691.430570[20, 162, 6]False0.045.046.4085370.6688547611.0False293623.00.02.9856570.6645801.02.0TrueTrueTrue
20052005.00.057.0{160, 0, 4, 7, 53, 62}{131, 3, 8, 137, 11, 142, 18, 158, 34, 35, 46,...({160, 0, 4, 7, 53, 62}, [{0, 1, 2, 3, 132, 8,...30.00.6362.0{(54, 55), (86, 87), (100, 101), (156, 157), (...{8, 107, 13, 145, 29, 17, 152, 60, 93, 95}{(54, 55), (86, 87), (100, 101), (156, 157), (...({0, 1, 2, 3, 132, 8, 142, 18, 152, 153, 158, ...[0, 162, 158, 2, 108, 70, 4, 71, 97, 1, 163, 1...146.0146.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3679, ({0, 128, 130, 3, 4, 132, 133, 8, 9, 10...(4006, ({6, 8, 13, 15, 16, 17, 22, 23, 24, 25,...0.1494631.443813[20, 162, 128]False0.045.045.3292680.6448647434.0False211212.00.02.7351880.6446861.02.0TrueTrueTrue
20122012.00.034.0{19, 121, 155, 0}{128, 129, 130, 133, 6, 7, 8, 9, 10, 12, 13, 1...({19, 121, 155, 0}, [{128, 129, 130, 0, 133, 1...66.00.8012.0{(54, 55), (86, 87), (92, 93), (100, 101), (15...{128, 133, 6, 8, 9, 12, 13, 20, 21, 32, 33, 35...{(54, 55), (86, 87), (92, 93), (100, 101), (15...({128, 129, 130, 0, 133, 134, 7, 12, 13, 15, 2...[0, 162, 0, 84, 83, 87, 81, 88, 80, 86, 79, 98...137.0137.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(4906, ({1, 2, 4, 5, 10, 13, 14, 15, 16, 23, 2...(5170, ({1, 2, 5, 6, 8, 9, 12, 13, 20, 21, 22,...0.1700941.269265[68, 138, 39]False0.071.059.5548780.8075329767.0False858989.00.08.4244710.8160651.02.0TrueTrueTrue
20422042.00.046.0{99, 6, 11, 142, 26, 126}{4, 5, 9, 138, 10, 12, 13, 15, 17, 20, 21, 34,...({99, 6, 11, 142, 26, 126}, [{4, 5, 9, 138, 10...30.00.6592.0{(54, 55), (86, 87), (92, 93), (156, 157), (40...{97, 129, 100, 133, 103, 7, 105, 78, 116, 53, ...{(54, 55), (86, 87), (92, 93), (156, 157), (40...({4, 5, 9, 138, 10, 12, 13, 15, 17, 20, 21, 34...[0, 160, 0, 132, 44, 4, 138, 28, 5, 57, 111, 1...145.0145.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3651, ({0, 1, 5, 6, 7, 8, 12, 13, 17, 20, 21,...(3940, ({7, 8, 11, 14, 16, 20, 21, 22, 23, 28,...0.1582841.455185[39, 70, 0]False0.041.044.4024390.6512367282.0False212400.00.03.4835280.6499071.02.0TrueTrueTrue
20442044.00.056.0{0, 129, 4, 14, 157, 62}{4, 5, 6, 7, 9, 10, 21, 29, 44, 45, 48, 49, 50...({0, 129, 4, 14, 157, 62}, [{4, 5, 6, 7, 9, 10...38.00.6522.0{(54, 55), (92, 93), (125, 126), (156, 157), (...{133, 134, 12, 144, 145, 18, 146, 147, 26, 154...{(54, 55), (92, 93), (125, 126), (156, 157), (...({4, 5, 6, 7, 9, 10, 21, 29, 44, 45, 48, 49, 5...[0, 153, 141, 20, 3, 138, 31, 150, 21, 67, 101...137.0137.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3504, ({4, 6, 7, 10, 11, 12, 13, 14, 16, 17, ...(3802, ({2, 6, 8, 12, 13, 15, 16, 17, 18, 19, ...0.2155611.478004[20, 162, 5]False0.050.042.5426830.6571886977.0False68496.00.03.7077900.6569861.02.0TrueTrueTrue
20132013.00.055.0{6, 11, 46, 143, 16, 159}{1, 2, 3, 14, 148, 22, 23, 24, 25, 26, 32, 33,...({6, 11, 46, 143, 16, 159}, [{0, 1, 2, 3, 140,...28.00.6242.0{(54, 55), (86, 87), (92, 93), (100, 101), (15...{4, 100, 104, 106, 138, 116, 153}{(54, 55), (86, 87), (92, 93), (100, 101), (15...({0, 1, 2, 3, 140, 14, 22, 23, 25, 29, 32, 33,...[0, 161, 162, 3, 49, 128, 0, 85, 84, 87, 83, 8...129.0129.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3484, ({1, 3, 5, 6, 9, 11, 13, 14, 16, 20, 21...(3801, ({0, 3, 9, 10, 14, 19, 20, 22, 26, 29, ...0.1251641.480398[80, 125, 129]False0.042.042.3475610.6331016945.0False116355.00.01.6129910.6291581.02.0TrueTrueTrue
20672067.00.054.0{128, 0, 2, 70, 10, 82}{140, 146, 148, 24, 25, 27, 29, 38, 40, 42, 48...({128, 0, 2, 70, 10, 82}, [{2, 3, 4, 5, 9, 146...24.00.6702.0{(65, 67), (86, 87), (156, 157), (40, 41), (72...{162, 100, 136, 43, 110, 144, 146, 116, 52, 12...{(65, 67), (86, 87), (156, 157), (40, 41), (72...({2, 3, 4, 5, 9, 146, 27, 38, 40, 42, 43, 49, ...[0, 162, 1, 105, 62, 2, 69, 98, 88, 77, 101, 6...141.0141.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3435, ({0, 1, 2, 8, 11, 12, 13, 17, 18, 19, 2...(3775, ({3, 8, 9, 10, 11, 12, 13, 14, 15, 18, ...0.1636011.479276[39, 70, 0]False0.041.042.4390240.6305456960.0False163839.00.02.2473270.6284541.02.0TrueTrueTrue
20622062.00.066.0{162, 130, 7, 140, 15, 49}{4, 5, 6, 8, 12, 13, 16, 17, 20, 34, 35, 45, 6...({162, 130, 7, 140, 15, 49}, [{4, 5, 6, 8, 12,...25.00.6332.0{(54, 55), (86, 87), (92, 93), (100, 101), (15...{160, 100, 101, 104, 48, 151, 152, 59, 157}{(54, 55), (86, 87), (92, 93), (100, 101), (15...({4, 5, 6, 8, 12, 13, 16, 17, 20, 34, 35, 45, ...[0, 161, 85, 0, 87, 84, 0, 162, 1, 88, 83, 93,...144.0144.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3515, ({0, 1, 2, 4, 5, 7, 10, 12, 15, 16, 18,...(3837, ({3, 5, 6, 10, 12, 13, 14, 15, 23, 24, ...0.0904661.471794[80, 125, 4]False0.042.043.0487800.6239797060.0False155845.00.01.0115850.6211671.02.0TrueTrueTrue
20522052.00.050.0{0, 129, 99, 143, 89, 155}{0, 1, 2, 3, 7, 136, 22, 24, 158, 31, 32, 33, ...({0, 129, 99, 143, 89, 155}, [{0, 1, 2, 3, 7, ...29.00.6512.0{(134, 137), (54, 55), (86, 87), (100, 101), (...{128, 7, 8, 10, 141, 144, 147, 149, 158, 30, 1...{(134, 137), (54, 55), (86, 87), (100, 101), (...({0, 1, 2, 3, 7, 136, 22, 24, 158, 31, 32, 33,...[0, 131, 44, 4, 117, 57, 1, 62, 116, 106, 76, ...142.0142.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3584, ({0, 1, 3, 5, 6, 8, 12, 16, 20, 22, 24,...(3867, ({2, 3, 6, 7, 8, 9, 14, 16, 17, 19, 21,...0.1979261.469176[39, 70, 128]False0.043.043.2621950.6399167095.0False144546.00.03.4821250.6413591.02.0TrueTrueTrue
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20682068.00.056.0{162, 132, 4, 72, 12}{13, 14, 15, 16, 17, 18, 19, 21, 26, 27, 33, 3...({162, 132, 4, 72, 12}, [{0, 12, 13, 26, 27, 2...37.00.6982.0{(86, 87), (125, 126), (156, 157), (40, 41), (...{101, 139, 45, 112, 114, 86, 118, 151}{(86, 87), (125, 126), (156, 157), (40, 41), (...({0, 12, 13, 26, 27, 28, 29, 33, 36, 40, 42, 4...[0, 163, 0, 101, 61, 11, 17, 149, 1, 150, 16, ...130.0130.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3811, ({0, 2, 3, 5, 14, 15, 20, 21, 26, 28, 2...(4123, ({0, 3, 7, 11, 15, 18, 20, 21, 22, 23, ...0.1125561.431169[20, 162, 132]False0.051.046.3597560.6974407603.0False163109.00.03.4587290.6892841.02.0TrueTrueTrue
20352035.00.052.0{162, 41, 14, 51, 24, 59}{4, 5, 6, 9, 10, 12, 13, 15, 16, 17, 146, 147,...({162, 41, 14, 51, 24, 59}, [{4, 5, 6, 9, 10, ...30.00.6462.0{(54, 55), (100, 101), (156, 157), (40, 41), (...{131, 132, 134, 135, 155, 46, 144, 146, 83, 30...{(54, 55), (100, 101), (156, 157), (40, 41), (...({4, 5, 6, 9, 10, 12, 13, 15, 16, 17, 146, 147...[0, 163, 2, 68, 103, 1, 105, 69, 1, 100, 67, 2...138.0138.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3648, ({0, 1, 4, 7, 9, 13, 15, 16, 18, 19, 22...(3928, ({7, 9, 15, 16, 17, 18, 19, 20, 21, 22,...0.1486201.458327[20, 162, 5]False0.047.044.1463410.6607297240.0False140215.00.02.7391140.6574461.02.0TrueTrueTrue
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20362036.00.051.0{0, 5, 40, 8, 156, 126}{11, 12, 13, 14, 16, 17, 24, 25, 27, 28, 29, 3...({0, 5, 40, 8, 156, 126}, [{4, 5, 102, 91, 108...29.00.6682.0{(65, 67), (54, 55), (125, 126), (156, 157), (...{159, 33, 34, 101, 102, 155, 108, 14, 15, 145,...{(65, 67), (54, 55), (125, 126), (156, 157), (...({4, 5, 102, 91, 108, 13, 14, 12, 81, 21, 24, ...[0, 142, 0, 115, 49, 2, 69, 95, 111, 57, 5, 16...146.0146.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(3789, ({3, 5, 6, 7, 10, 12, 14, 18, 21, 23, 2...(4135, ({0, 1, 2, 3, 4, 6, 11, 12, 14, 15, 16,...0.0945681.428400[20, 162, 97]False0.042.046.5853660.6537857640.0False409071.00.03.2463700.6523701.02.0TrueTrueTrue
20332033.00.045.0{130, 4, 136, 22, 155, 157}{5, 6, 7, 8, 11, 12, 13, 14, 15, 27, 34, 35, 3...({130, 4, 136, 22, 155, 157}, [{0, 1, 2, 3, 6,...41.00.7382.0{(54, 55), (86, 87), (100, 101), (125, 126), (...{32, 100, 27, 106, 46, 84, 55, 24, 91, 93}{(54, 55), (86, 87), (100, 101), (125, 126), (...({0, 1, 2, 3, 6, 18, 19, 25, 28, 33, 36, 46, 4...[0, 85, 84, 86, 83, 89, 82, 90, 81, 0, 87, 80,...140.0140.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(4256, ({0, 2, 3, 4, 5, 6, 11, 15, 18, 24, 26,...(4556, ({0, 2, 3, 4, 7, 8, 9, 10, 14, 15, 16, ...0.1359811.368248[20, 162, 6]False0.054.051.4878050.7206928444.0False859669.00.05.6060390.7216081.02.0TrueTrueTrue
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21532153.01.060.0{136, 8, 108, 143, 154}{0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, 3...({136, 8, 108, 143, 154}, [{0, 1, 130, 3, 2, 1...40.00.7102.0{(54, 55), (92, 93), (156, 157), (40, 41), (72...{10, 75, 91, 45, 77, 86, 123, 124}{(54, 55), (92, 93), (156, 157), (40, 41), (72...({0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, ...[0, 153, 101, 67, 1, 71, 100, 0, 145, 29, 2, 7...143.0143.0{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...(4084, ({0, 129, 3, 4, 131, 133, 7, 134, 9, 10...(4641, ({0, 1, 2, 4, 11, 12, 14, 15, 24, 25, 2...0.0623551.360766[50, 96, 163]False0.054.052.0975610.7217418544.0False592404.00.03.8480970.7178571.02.0TrueTrueTrue
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\n"," "],"text/plain":[" Subject Schizophrenic Approximation and Heuristics Node Connectivity \\\n","2019 2019.0 0.0 43.0 \n","2024 2024.0 0.0 62.0 \n","2022 2022.0 0.0 42.0 \n","2015 2015.0 0.0 60.0 \n","2025 2025.0 0.0 50.0 \n","2017 2017.0 0.0 35.0 \n","2010 2010.0 0.0 42.0 \n","2020 2020.0 0.0 47.0 \n","2026 2026.0 0.0 51.0 \n","2023 2023.0 0.0 58.0 \n","2001 2001.0 0.0 52.0 \n","2018 2018.0 0.0 48.0 \n","2007 2007.0 0.0 53.0 \n","2002 2002.0 0.0 50.0 \n","2009 2009.0 0.0 41.0 \n","2016 2016.0 0.0 53.0 \n","2006 2006.0 0.0 63.0 \n","2003 2003.0 0.0 44.0 \n","2008 2008.0 0.0 45.0 \n","2014 2014.0 0.0 58.0 \n","2021 2021.0 0.0 63.0 \n","2004 2004.0 0.0 51.0 \n","2011 2011.0 0.0 51.0 \n","2005 2005.0 0.0 57.0 \n","2012 2012.0 0.0 34.0 \n","2042 2042.0 0.0 46.0 \n","2044 2044.0 0.0 56.0 \n","2013 2013.0 0.0 55.0 \n","2067 2067.0 0.0 54.0 \n","2062 2062.0 0.0 66.0 \n","2052 2052.0 0.0 50.0 \n","2070 2070.0 0.0 56.0 \n","2068 2068.0 0.0 56.0 \n","2035 2035.0 0.0 52.0 \n","2030 2030.0 0.0 38.0 \n","2036 2036.0 0.0 51.0 \n","2033 2033.0 0.0 45.0 \n","2029 2029.0 0.0 62.0 \n","2038 2038.0 0.0 47.0 \n","2063 2063.0 0.0 63.0 \n","2061 2061.0 0.0 52.0 \n","2059 2059.0 0.0 57.0 \n","2040 2040.0 0.0 58.0 \n","2056 2056.0 0.0 59.0 \n","2048 2048.0 0.0 54.0 \n","2073 2073.0 0.0 56.0 \n","2076 2076.0 0.0 51.0 \n","2039 2039.0 0.0 48.0 \n","2051 2051.0 0.0 44.0 \n","2049 2049.0 0.0 60.0 \n","2075 2075.0 0.0 44.0 \n","2043 2043.0 0.0 60.0 \n","2069 2069.0 0.0 50.0 \n","2027 2027.0 0.0 45.0 \n","2074 2074.0 0.0 63.0 \n","2058 2058.0 0.0 34.0 \n","2055 2055.0 0.0 56.0 \n","2065 2065.0 0.0 49.0 \n","2053 2053.0 0.0 51.0 \n","2046 2046.0 0.0 59.0 \n","2072 2072.0 0.0 45.0 \n","2034 2034.0 0.0 44.0 \n","2041 2041.0 0.0 41.0 \n","2057 2057.0 0.0 55.0 \n","2031 2031.0 0.0 61.0 \n","2066 2066.0 0.0 56.0 \n","2064 2064.0 0.0 57.0 \n","2032 2032.0 0.0 47.0 \n","2054 2054.0 0.0 48.0 \n","2071 2071.0 0.0 43.0 \n","2060 2060.0 0.0 53.0 \n","2028 2028.0 0.0 51.0 \n","2045 2045.0 0.0 63.0 \n","2050 2050.0 0.0 51.0 \n","2047 2047.0 0.0 59.0 \n","2037 2037.0 0.0 52.0 \n","2099 2099.0 0.0 58.0 \n","2114 2114.0 0.0 48.0 \n","2108 2108.0 0.0 38.0 \n","2104 2104.0 0.0 60.0 \n","2078 2078.0 0.0 49.0 \n","2101 2101.0 0.0 56.0 \n","2110 2110.0 0.0 28.0 \n","2081 2081.0 0.0 53.0 \n","2087 2087.0 0.0 52.0 \n","2121 2121.0 0.0 65.0 \n","2092 2092.0 0.0 41.0 \n","2079 2079.0 0.0 57.0 \n","2080 2080.0 0.0 56.0 \n","2113 2113.0 0.0 59.0 \n","2094 2094.0 0.0 52.0 \n","2112 2112.0 0.0 51.0 \n","2091 2091.0 0.0 61.0 \n","2090 2090.0 0.0 49.0 \n","2105 2105.0 0.0 51.0 \n","2102 2102.0 0.0 36.0 \n","2088 2088.0 0.0 53.0 \n","2109 2109.0 0.0 59.0 \n","2084 2084.0 0.0 57.0 \n","2098 2098.0 0.0 50.0 \n","2118 2118.0 0.0 57.0 \n","2119 2119.0 0.0 40.0 \n","2115 2115.0 0.0 42.0 \n","2086 2086.0 0.0 58.0 \n","2124 2124.0 1.0 53.0 \n","2100 2100.0 0.0 54.0 \n","2117 2117.0 0.0 60.0 \n","2103 2103.0 0.0 53.0 \n","2125 2125.0 1.0 43.0 \n","2085 2085.0 0.0 42.0 \n","2120 2120.0 0.0 51.0 \n","2097 2097.0 0.0 54.0 \n","2089 2089.0 0.0 38.0 \n","2107 2107.0 0.0 56.0 \n","2106 2106.0 0.0 58.0 \n","2095 2095.0 0.0 53.0 \n","2093 2093.0 0.0 40.0 \n","2083 2083.0 0.0 54.0 \n","2122 2122.0 0.0 59.0 \n","2111 2111.0 0.0 49.0 \n","2082 2082.0 0.0 54.0 \n","2126 2126.0 1.0 49.0 \n","2116 2116.0 0.0 59.0 \n","2096 2096.0 0.0 59.0 \n","2077 2077.0 0.0 57.0 \n","2123 2123.0 1.0 38.0 \n","2148 2148.0 1.0 45.0 \n","2155 2155.0 1.0 22.0 \n","2130 2130.0 1.0 60.0 \n","2171 2171.0 1.0 23.0 \n","2129 2129.0 1.0 53.0 \n","2151 2151.0 1.0 39.0 \n","2145 2145.0 1.0 51.0 \n","2142 2142.0 1.0 57.0 \n","2156 2156.0 1.0 47.0 \n","2143 2143.0 1.0 54.0 \n","2167 2167.0 1.0 56.0 \n","2144 2144.0 1.0 53.0 \n","2147 2147.0 1.0 49.0 \n","2152 2152.0 1.0 56.0 \n","2163 2163.0 1.0 54.0 \n","2138 2138.0 1.0 63.0 \n","2159 2159.0 1.0 58.0 \n","2158 2158.0 1.0 38.0 \n","2134 2134.0 1.0 40.0 \n","2169 2169.0 1.0 45.0 \n","2136 2136.0 1.0 45.0 \n","2137 2137.0 1.0 44.0 \n","2166 2166.0 1.0 46.0 \n","2170 2170.0 1.0 52.0 \n","2128 2128.0 1.0 50.0 \n","2149 2149.0 1.0 46.0 \n","2172 2172.0 1.0 44.0 \n","2168 2168.0 1.0 59.0 \n","2160 2160.0 1.0 54.0 \n","2154 2154.0 1.0 25.0 \n","2161 2161.0 1.0 59.0 \n","2140 2140.0 1.0 53.0 \n","2164 2164.0 1.0 58.0 \n","2165 2165.0 1.0 57.0 \n","2146 2146.0 1.0 66.0 \n","2150 2150.0 1.0 38.0 \n","2141 2141.0 1.0 60.0 \n","2131 2131.0 1.0 56.0 \n","2135 2135.0 1.0 58.0 \n","2127 2127.0 1.0 47.0 \n","2132 2132.0 1.0 41.0 \n","2162 2162.0 1.0 52.0 \n","2157 2157.0 1.0 59.0 \n","2139 2139.0 1.0 47.0 \n","2133 2133.0 1.0 57.0 \n","2153 2153.0 1.0 60.0 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","2019 {128, 0, 4, 147, 89, 156} \n","2024 {33, 4, 134, 8, 12, 56} \n","2022 {1, 100, 5, 36, 159} \n","2015 {128, 0, 76, 148, 29} \n","2025 {130, 100, 5, 6, 9, 154} \n","2017 {32, 101, 137, 12, 151, 125} \n","2010 {66, 130, 4, 106, 75, 124} \n","2020 {129, 4, 102, 11, 87, 121} \n","2026 {0, 4, 38, 144, 19, 58} \n","2023 {128, 68, 15, 145, 83, 28} \n","2001 {0, 162, 99, 130, 47, 56} \n","2018 {0, 1, 163, 69, 139, 26} \n","2007 {128, 3, 7, 136, 145, 86} \n","2002 {0, 4, 138, 52, 93} \n","2009 {128, 0, 69, 137, 140} \n","2016 {128, 1, 0, 5, 78, 112} \n","2006 {67, 163, 135, 14, 57, 158} \n","2003 {128, 131, 6, 24, 154, 156} \n","2008 {106, 123, 78, 15, 58, 27} \n","2014 {0, 129, 1, 4, 119} \n","2021 {163, 9, 11, 19, 116, 126} \n","2004 {4, 8, 75, 44, 13, 95} \n","2011 {65, 38, 7, 136, 11, 77} \n","2005 {160, 0, 4, 7, 53, 62} \n","2012 {19, 121, 155, 0} \n","2042 {99, 6, 11, 142, 26, 126} \n","2044 {0, 129, 4, 14, 157, 62} \n","2013 {6, 11, 46, 143, 16, 159} \n","2067 {128, 0, 2, 70, 10, 82} \n","2062 {162, 130, 7, 140, 15, 49} \n","2052 {0, 129, 99, 143, 89, 155} \n","2070 {0, 129, 101, 70, 7} \n","2068 {162, 132, 4, 72, 12} \n","2035 {162, 41, 14, 51, 24, 59} \n","2030 {128, 0, 132, 122, 63} \n","2036 {0, 5, 40, 8, 156, 126} \n","2033 {130, 4, 136, 22, 155, 157} \n","2029 {0, 4, 7, 56, 62} \n","2038 {160, 1, 7, 42, 157} \n","2063 {128, 0, 74, 12, 142} \n","2061 {0, 129, 34, 7, 55} \n","2059 {0, 4, 38, 9, 153, 28} \n","2040 {8, 41, 16, 24, 154, 93} \n","2056 {128, 0, 68, 14, 93} \n","2048 {72, 45, 48, 121, 90, 157, 62} \n","2073 {0, 130, 5, 101, 16} \n","2076 {4, 7, 139, 152, 57} \n","2039 {0, 4, 137, 90, 156} \n","2051 {129, 100, 76, 116, 23, 155} \n","2049 {64, 0, 36, 11, 156} \n","2075 {0, 33, 129, 143, 63} \n","2043 {2, 133, 70, 78, 115} \n","2069 {128, 1, 0, 7, 81, 60} \n","2027 {64, 1, 128, 15, 51} \n","2074 {128, 0, 66, 78, 28} \n","2058 {0, 5, 70, 141, 126} \n","2055 {0, 129, 135, 142, 112, 154} \n","2065 {0, 130, 4, 41, 145, 89} \n","2053 {0, 3, 42, 60, 159} \n","2046 {160, 3, 101, 12, 19} \n","2072 {0, 128, 8, 108, 155} \n","2034 {0, 1, 3, 154, 126} \n","2041 {0, 162, 4, 14, 145} \n","2057 {128, 131, 4, 8, 75, 24} \n","2031 {129, 131, 37, 6, 54, 155} \n","2066 {64, 1, 133, 10, 24} \n","2064 {0, 129, 100, 43, 51} \n","2032 {128, 0, 70, 7, 141, 118} \n","2054 {132, 100, 138, 12, 154, 123} \n","2071 {0, 129, 4, 74, 151} \n","2060 {128, 0, 163, 4, 38, 153} \n","2028 {160, 129, 0, 1, 54} \n","2045 {0, 97, 12, 94, 63} \n","2050 {2, 132, 9, 61, 126} \n","2047 {0, 163, 5, 138, 60} \n","2037 {0, 162, 13, 46, 126} \n","2099 {0, 1, 105, 114, 19} \n","2114 {0, 130, 5, 24, 153} \n","2108 {0, 163, 9, 138, 111} \n","2104 {2, 132, 136, 111, 52, 31} \n","2078 {128, 66, 7, 44, 141, 56} \n","2101 {64, 128, 1, 38, 137, 16} \n","2110 {0, 98, 130, 101, 139} \n","2081 {0, 4, 43, 143, 79} \n","2087 {0, 1, 130, 141, 114} \n","2121 {0, 129, 5, 70, 138, 59} \n","2092 {0, 129, 5, 39, 121, 154} \n","2079 {0, 130, 132, 20, 119} \n","2080 {0, 161, 99, 7, 149, 57} \n","2113 {0, 129, 4, 72, 142, 119} \n","2094 {128, 0, 14, 51, 59} \n","2112 {0, 129, 7, 58, 62} \n","2091 {161, 8, 11, 108, 23, 155} \n","2090 {97, 135, 15, 113, 22, 151} \n","2105 {97, 130, 3, 100, 6, 135} \n","2102 {0, 129, 104, 137, 79} \n","2088 {0, 8, 41, 14, 146} \n","2109 {0, 101, 7, 11, 150, 55} \n","2084 {0, 131, 36, 10, 51} \n","2098 {153, 2, 6, 121, 31} \n","2118 {128, 0, 66, 29, 94} \n","2119 {131, 14, 148, 152, 58} \n","2115 {0, 128, 6, 107, 19} \n","2086 {130, 14, 20, 22, 56, 31} \n","2124 {4, 133, 71, 85, 156} \n","2100 {0, 4, 7, 149, 95} \n","2117 {0, 139, 18, 90, 123} \n","2103 {1, 66, 163, 4, 11, 139} \n","2125 {0, 163, 5, 22, 89} \n","2085 {101, 7, 135, 41, 157} \n","2120 {68, 135, 137, 105, 75, 23} \n","2097 {97, 4, 8, 12, 142, 151} \n","2089 {0, 130, 5, 38, 8, 139} \n","2107 {0, 129, 7, 40, 157, 93} \n","2106 {0, 4, 136, 78, 48} \n","2095 {96, 128, 160, 107, 11, 22} \n","2093 {0, 4, 138, 153, 154} \n","2083 {0, 4, 81, 24, 155} \n","2122 {128, 161, 0, 131, 148, 59} \n","2111 {0, 99, 4, 142, 17} \n","2082 {0, 67, 133, 7, 141, 29} \n","2126 {0, 130, 7, 108, 151, 156} \n","2116 {0, 130, 132, 7, 71} \n","2096 {0, 130, 7, 137, 24} \n","2077 {0, 129, 35, 70, 119} \n","2123 {129, 6, 135, 11, 159} \n","2148 {0, 133, 37, 138, 15, 158} \n","2155 {0, 129, 163, 113, 63} \n","2130 {0, 133, 138, 16, 145} \n","2171 {65, 99, 139, 53, 25} \n","2129 {133, 107, 18, 154, 61} \n","2151 {128, 1, 131, 140, 153} \n","2145 {160, 0, 5, 75, 14} \n","2142 {0, 1, 4, 49, 148} \n","2156 {0, 4, 102, 90, 155} \n","2143 {128, 0, 8, 20, 156, 61} \n","2167 {0, 129, 135, 137, 108, 150} \n","2144 {97, 100, 11, 81, 59} \n","2147 {130, 4, 136, 53, 152, 91} \n","2152 {161, 129, 2, 6, 155, 126} \n","2163 {0, 99, 4, 62, 31} \n","2138 {160, 0, 128, 14, 19} \n","2159 {0, 3, 163, 5, 135, 22} \n","2158 {0, 138, 12, 154, 94} \n","2134 {128, 0, 35, 18, 19} \n","2169 {128, 2, 9, 141, 94} \n","2136 {0, 100, 4, 139, 12, 156} \n","2137 {160, 1, 128, 7, 59} \n","2166 {128, 0, 67, 5, 139, 47} \n","2170 {128, 0, 163, 137, 111, 145} \n","2128 {0, 132, 69, 9, 49} \n","2149 {17, 82, 50, 151, 157} \n","2172 {135, 42, 10, 141, 53} \n","2168 {0, 4, 133, 70, 39, 150} \n","2160 {0, 137, 139, 81, 56} \n","2154 {128, 163, 8, 10, 15, 60} \n","2161 {99, 6, 15, 144, 22} \n","2140 {0, 162, 6, 143} \n","2164 {0, 1, 4, 14, 20, 127} \n","2165 {1, 101, 134, 24, 125} \n","2146 {0, 98, 4, 135, 141, 158} \n","2150 {128, 0, 4, 47, 157} \n","2141 {0, 4, 100, 13, 154} \n","2131 {131, 69, 8, 43, 15, 157} \n","2135 {1, 130, 131, 42, 152} \n","2127 {161, 135, 12, 48, 29} \n","2132 {0, 130, 131, 138, 19} \n","2162 {131, 36, 5, 7, 142, 28} \n","2157 {0, 1, 163, 16, 124} \n","2139 {128, 161, 135, 39, 9, 56} \n","2133 {100, 18, 122, 156, 30} \n","2153 {136, 8, 108, 143, 154} \n","\n"," Approximation and Heuristics Max Cliques \\\n","2019 {11, 13, 14, 15, 16, 17, 21, 22, 23, 26, 27, 2... \n","2024 {5, 6, 7, 10, 145, 44, 45, 46, 47, 48, 51, 52,... \n","2022 {0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 32... \n","2015 {6, 7, 8, 9, 10, 145, 146, 147, 21, 150, 157, ... \n","2025 {129, 8, 141, 19, 22, 23, 28, 29, 31, 32, 33, ... \n","2017 {6, 8, 9, 10, 17, 146, 147, 20, 21, 19, 18, 30... \n","2010 {12, 13, 14, 15, 16, 17, 25, 26, 28, 29, 36, 3... \n","2020 {130, 11, 13, 15, 16, 17, 151, 27, 29, 32, 34,... \n","2026 {2, 8, 140, 141, 148, 149, 22, 23, 24, 26, 27,... \n","2023 {7, 9, 10, 13, 15, 17, 21, 152, 35, 42, 66, 74... \n","2001 {10, 148, 149, 22, 151, 24, 25, 26, 27, 28, 29... \n","2018 {1, 2, 131, 4, 5, 6, 10, 144, 146, 19, 18, 21,... \n","2007 {4, 5, 6, 9, 10, 13, 15, 16, 17, 21, 150, 28, ... \n","2002 {4, 5, 6, 7, 12, 13, 145, 147, 21, 150, 161, 3... \n","2009 {9, 10, 12, 13, 15, 16, 20, 21, 26, 27, 29, 35... \n","2016 {11, 12, 13, 14, 15, 18, 19, 20, 21, 32, 33, 3... \n","2006 {138, 139, 12, 13, 15, 17, 146, 147, 20, 19, 1... \n","2003 {128, 130, 133, 134, 135, 11, 12, 13, 27, 32, ... \n","2008 {4, 5, 135, 136, 11, 12, 13, 16, 145, 18, 19, ... \n","2014 {5, 6, 11, 12, 13, 14, 18, 34, 35, 43, 45, 65,... \n","2021 {0, 132, 133, 134, 135, 8, 7, 6, 5, 4, 143, 14... \n","2004 {1, 2, 3, 6, 17, 27, 28, 29, 40, 46, 48, 50, 5... \n","2011 {132, 5, 134, 11, 12, 13, 16, 18, 34, 35, 42, ... \n","2005 {131, 3, 8, 137, 11, 142, 18, 158, 34, 35, 46,... \n","2012 {128, 129, 130, 133, 6, 7, 8, 9, 10, 12, 13, 1... \n","2042 {4, 5, 9, 138, 10, 12, 13, 15, 17, 20, 21, 34,... \n","2044 {4, 5, 6, 7, 9, 10, 21, 29, 44, 45, 48, 49, 50... \n","2013 {1, 2, 3, 14, 148, 22, 23, 24, 25, 26, 32, 33,... \n","2067 {140, 146, 148, 24, 25, 27, 29, 38, 40, 42, 48... \n","2062 {4, 5, 6, 8, 12, 13, 16, 17, 20, 34, 35, 45, 6... \n","2052 {0, 1, 2, 3, 7, 136, 22, 24, 158, 31, 32, 33, ... \n","2070 {141, 149, 22, 23, 25, 27, 28, 29, 32, 33, 38,... \n","2068 {13, 14, 15, 16, 17, 18, 19, 21, 26, 27, 33, 3... \n","2035 {4, 5, 6, 9, 10, 12, 13, 15, 16, 17, 146, 147,... \n","2030 {12, 13, 14, 15, 144, 17, 146, 147, 20, 16, 27... \n","2036 {11, 12, 13, 14, 16, 17, 24, 25, 27, 28, 29, 3... \n","2033 {5, 6, 7, 8, 11, 12, 13, 14, 15, 27, 34, 35, 3... \n","2029 {0, 1, 2, 3, 140, 141, 23, 24, 25, 26, 28, 156... \n","2038 {4, 133, 134, 6, 5, 9, 10, 11, 12, 13, 14, 16,... \n","2063 {0, 1, 2, 131, 3, 140, 14, 144, 23, 25, 28, 29... \n","2061 {0, 1, 2, 3, 4, 9, 10, 13, 144, 145, 146, 22, ... \n","2059 {14, 15, 16, 17, 146, 19, 20, 21, 18, 156, 159... \n","2040 {5, 7, 8, 9, 138, 10, 146, 147, 159, 34, 44, 4... \n","2056 {133, 134, 7, 136, 9, 138, 11, 12, 10, 8, 33, ... \n","2048 {4, 133, 134, 12, 13, 15, 17, 20, 35, 42, 57, ... \n","2073 {128, 129, 7, 8, 9, 10, 11, 13, 14, 15, 17, 14... \n","2076 {129, 132, 133, 134, 137, 143, 144, 145, 147, ... \n","2039 {133, 6, 5, 10, 13, 17, 19, 26, 27, 28, 34, 35... \n","2051 {128, 1, 2, 0, 132, 133, 134, 135, 136, 6, 5, ... \n","2049 {4, 5, 11, 12, 13, 15, 16, 17, 26, 27, 29, 34,... \n","2075 {0, 1, 2, 131, 132, 5, 134, 6, 136, 4, 3, 144,... \n","2043 {8, 9, 138, 10, 20, 21, 22, 28, 156, 31, 40, 4... \n","2069 {134, 144, 145, 146, 147, 150, 151, 152, 158, ... \n","2027 {4, 5, 136, 12, 16, 22, 155, 33, 35, 37, 44, 4... \n","2074 {2, 3, 140, 141, 15, 18, 19, 23, 25, 29, 31, 3... \n","2058 {137, 144, 149, 151, 152, 153, 26, 27, 30, 161... \n","2055 {7, 8, 9, 10, 146, 147, 150, 30, 159, 31, 161,... \n","2065 {131, 132, 133, 12, 13, 148, 24, 25, 27, 32, 3... \n","2053 {6, 7, 9, 18, 20, 48, 51, 64, 65, 66, 67, 76, ... \n","2046 {4, 5, 7, 8, 9, 10, 18, 20, 45, 46, 47, 48, 49... \n","2072 {3, 10, 11, 13, 14, 15, 24, 28, 29, 32, 33, 34... \n","2034 {4, 133, 134, 7, 6, 137, 10, 9, 5, 16, 19, 21,... \n","2041 {133, 27, 28, 29, 34, 35, 37, 38, 39, 40, 41, ... \n","2057 {5, 7, 9, 10, 17, 146, 147, 20, 21, 28, 34, 42... \n","2031 {5, 11, 12, 13, 16, 17, 21, 34, 35, 36, 43, 44... \n","2066 {130, 137, 138, 139, 13, 142, 16, 145, 17, 149... \n","2064 {1, 2, 131, 132, 3, 134, 7, 144, 145, 19, 22, ... \n","2032 {6, 10, 12, 13, 18, 19, 154, 29, 35, 42, 44, 4... \n","2054 {5, 6, 9, 10, 144, 145, 146, 147, 19, 21, 17, ... \n","2071 {133, 7, 8, 9, 138, 11, 12, 13, 14, 15, 16, 17... \n","2060 {1, 2, 3, 5, 7, 8, 9, 10, 144, 18, 49, 76, 77,... \n","2028 {3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 18, 20,... \n","2045 {128, 5, 134, 6, 12, 13, 16, 22, 34, 35, 39, 4... \n","2050 {11, 12, 13, 18, 19, 152, 153, 30, 34, 35, 36,... \n","2047 {11, 12, 13, 14, 15, 146, 148, 21, 150, 20, 15... \n","2037 {7, 139, 141, 145, 147, 22, 151, 23, 26, 155, ... \n","2099 {128, 0, 130, 2, 11, 13, 15, 145, 24, 29, 32, ... \n","2114 {134, 13, 14, 15, 16, 26, 27, 28, 29, 30, 34, ... \n","2108 {4, 5, 6, 11, 12, 13, 14, 15, 145, 18, 17, 20,... \n","2104 {1, 4, 5, 6, 12, 14, 22, 26, 33, 162, 35, 39, ... \n","2078 {11, 12, 13, 14, 15, 16, 17, 148, 21, 150, 20,... \n","2101 {4, 5, 6, 9, 146, 44, 45, 49, 50, 51, 64, 65, ... \n","2110 {128, 0, 4, 5, 10, 11, 12, 13, 16, 17, 146, 20... \n","2081 {4, 5, 6, 9, 12, 13, 14, 15, 16, 17, 20, 158, ... \n","2087 {2, 3, 4, 5, 9, 10, 16, 20, 21, 25, 27, 156, 2... \n","2121 {0, 1, 7, 136, 8, 10, 139, 141, 144, 30, 31, 1... \n","2092 {25, 27, 28, 29, 34, 35, 38, 40, 41, 42, 47, 4... \n","2079 {16, 18, 19, 20, 34, 35, 42, 48, 56, 57, 59, 6... \n","2080 {138, 12, 13, 14, 15, 16, 145, 146, 17, 20, 21... \n","2113 {4, 5, 6, 9, 10, 18, 147, 20, 21, 19, 44, 45, ... \n","2094 {5, 6, 9, 10, 18, 19, 20, 21, 29, 44, 45, 48, ... \n","2112 {8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 21, 150... \n","2091 {0, 1, 2, 131, 3, 135, 148, 152, 28, 29, 30, 1... \n","2090 {128, 1, 130, 3, 2, 0, 137, 139, 147, 152, 153... \n","2105 {0, 129, 2, 1, 8, 140, 141, 148, 149, 22, 23, ... \n","2102 {130, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 14... \n","2088 {133, 11, 13, 16, 17, 26, 27, 28, 29, 34, 35, ... \n","2109 {130, 134, 135, 24, 25, 34, 35, 45, 46, 47, 48... \n","2084 {7, 9, 138, 146, 19, 148, 21, 153, 154, 155, 3... \n","2098 {130, 141, 13, 16, 17, 19, 24, 25, 26, 28, 29,... \n","2118 {3, 5, 6, 8, 9, 10, 142, 144, 145, 26, 28, 158... \n","2119 {140, 22, 25, 27, 28, 29, 31, 36, 37, 39, 42, ... \n","2115 {0, 1, 2, 3, 139, 140, 22, 23, 24, 26, 30, 31,... \n","2086 {4, 6, 8, 9, 10, 12, 145, 34, 35, 44, 45, 48, ... \n","2124 {128, 6, 7, 9, 10, 11, 13, 14, 16, 17, 19, 21,... \n","2100 {128, 131, 4, 5, 6, 10, 16, 18, 20, 21, 34, 35... \n","2117 {6, 11, 12, 13, 14, 15, 17, 18, 21, 34, 35, 44... \n","2103 {8, 9, 13, 17, 150, 22, 153, 26, 30, 31, 40, 4... \n","2125 {136, 27, 28, 29, 34, 35, 36, 37, 38, 40, 41, ... \n","2085 {129, 11, 12, 13, 14, 144, 17, 16, 20, 21, 28,... \n","2120 {129, 133, 7, 8, 9, 146, 147, 19, 26, 33, 44, ... \n","2097 {131, 132, 133, 134, 6, 137, 144, 145, 19, 158... \n","2089 {10, 13, 14, 15, 17, 19, 21, 22, 151, 29, 33, ... \n","2107 {5, 6, 10, 12, 14, 17, 19, 20, 21, 34, 35, 44,... \n","2106 {4, 5, 6, 11, 16, 17, 21, 34, 35, 44, 45, 62, ... \n","2095 {141, 16, 18, 147, 20, 149, 21, 151, 19, 26, 2... \n","2093 {1, 2, 3, 138, 139, 140, 141, 11, 148, 149, 22... \n","2083 {129, 139, 140, 141, 14, 16, 17, 20, 149, 150,... \n","2122 {135, 8, 9, 10, 11, 12, 13, 7, 15, 16, 17, 146... \n","2111 {136, 8, 138, 139, 140, 13, 14, 15, 11, 148, 1... \n","2082 {5, 6, 10, 139, 15, 146, 147, 21, 29, 31, 44, ... \n","2126 {11, 12, 13, 15, 16, 17, 146, 19, 20, 21, 34, ... \n","2116 {131, 5, 6, 10, 144, 18, 19, 21, 161, 44, 45, ... \n","2096 {5, 6, 10, 11, 144, 145, 18, 147, 19, 44, 45, ... \n","2077 {128, 130, 133, 6, 143, 144, 28, 157, 49, 50, ... \n","2123 {0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 146, 23, 26, 2... \n","2148 {4, 5, 6, 13, 16, 145, 146, 147, 17, 21, 22, 2... \n","2155 {6, 7, 8, 10, 146, 19, 20, 21, 18, 44, 45, 51,... \n","2130 {0, 1, 2, 3, 6, 137, 11, 144, 152, 153, 27, 28... \n","2171 {128, 129, 130, 135, 9, 10, 12, 13, 14, 15, 14... \n","2129 {132, 5, 4, 7, 9, 10, 144, 145, 20, 21, 157, 1... \n","2151 {129, 4, 5, 6, 9, 10, 12, 13, 14, 16, 148, 21,... \n","2145 {133, 6, 5, 137, 13, 16, 17, 21, 150, 152, 34,... \n","2142 {4, 5, 6, 7, 8, 9, 12, 13, 16, 17, 146, 147, 1... \n","2156 {130, 4, 5, 6, 9, 11, 13, 14, 16, 17, 18, 19, ... \n","2143 {1, 2, 4, 134, 6, 18, 27, 28, 29, 37, 40, 41, ... \n","2167 {128, 4, 5, 12, 13, 14, 15, 16, 17, 20, 21, 30... \n","2144 {128, 129, 3, 133, 6, 7, 5, 9, 10, 15, 19, 20,... \n","2147 {10, 13, 16, 17, 18, 20, 21, 45, 56, 57, 66, 6... \n","2152 {1, 2, 3, 4, 9, 10, 149, 23, 154, 28, 29, 32, ... \n","2163 {1, 2, 3, 23, 24, 25, 26, 27, 28, 29, 32, 38, ... \n","2138 {4, 5, 6, 137, 10, 11, 9, 13, 16, 17, 146, 19,... \n","2159 {6, 8, 9, 10, 14, 16, 145, 146, 147, 20, 21, 1... \n","2158 {3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28, 29,... \n","2134 {131, 134, 11, 12, 13, 14, 15, 16, 17, 21, 27,... \n","2169 {4, 5, 6, 7, 11, 12, 13, 144, 17, 16, 21, 34, ... \n","2136 {5, 6, 7, 9, 11, 15, 16, 17, 146, 18, 20, 21, ... \n","2137 {12, 13, 16, 17, 147, 28, 30, 34, 36, 41, 42, ... \n","2166 {13, 14, 16, 17, 21, 22, 23, 24, 32, 33, 34, 3... \n","2170 {16, 17, 23, 25, 27, 28, 29, 32, 34, 35, 36, 4... \n","2128 {2, 10, 12, 13, 14, 15, 16, 17, 28, 32, 34, 35... \n","2149 {130, 138, 140, 14, 144, 146, 147, 149, 151, 3... \n","2172 {133, 134, 7, 8, 9, 10, 6, 13, 16, 17, 20, 21,... \n","2168 {129, 4, 5, 6, 11, 12, 13, 15, 16, 17, 21, 158... \n","2160 {132, 134, 6, 9, 10, 18, 21, 23, 34, 35, 44, 5... \n","2154 {4, 6, 9, 11, 12, 16, 147, 28, 161, 34, 35, 44... \n","2161 {1, 2, 3, 6, 7, 9, 10, 145, 19, 21, 28, 29, 36... \n","2140 {128, 130, 11, 12, 14, 16, 17, 18, 19, 20, 21,... \n","2164 {134, 16, 17, 25, 26, 27, 28, 29, 34, 35, 36, ... \n","2165 {5, 6, 9, 10, 11, 18, 19, 34, 35, 40, 42, 44, ... \n","2146 {10, 14, 15, 16, 17, 146, 20, 21, 34, 35, 42, ... \n","2150 {7, 8, 9, 10, 13, 16, 17, 19, 20, 21, 28, 34, ... \n","2141 {4, 5, 6, 9, 16, 17, 20, 21, 34, 44, 48, 50, 5... \n","2131 {2, 131, 3, 9, 10, 18, 37, 40, 50, 51, 52, 54,... \n","2135 {1, 2, 3, 133, 6, 7, 136, 9, 10, 21, 28, 156, ... \n","2127 {1, 2, 3, 4, 7, 8, 9, 138, 139, 140, 141, 14, ... \n","2132 {4, 5, 9, 10, 11, 12, 13, 14, 15, 146, 26, 34,... \n","2162 {20, 21, 151, 162, 46, 48, 52, 53, 58, 67, 76,... \n","2157 {5, 135, 136, 9, 138, 139, 140, 141, 7, 146, 1... \n","2139 {4, 5, 6, 7, 144, 17, 16, 147, 20, 21, 151, 15... \n","2133 {0, 129, 130, 3, 2, 1, 8, 15, 22, 23, 24, 25, ... \n","2153 {0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, 3... \n","\n"," Approximation and Heuristics Clique Removal \\\n","2019 ({128, 0, 4, 147, 89, 156}, [{4, 133, 6, 5, 16... \n","2024 ({33, 4, 134, 8, 12, 56}, [{0, 1, 2, 131, 3, 6... \n","2022 ({1, 100, 5, 36, 159}, [{0, 1, 2, 131, 4, 133,... \n","2015 ({128, 0, 76, 148, 29}, [{128, 129, 134, 12, 1... \n","2025 ({130, 100, 5, 6, 9, 154}, [{0, 1, 2, 3, 4, 14... \n","2017 ({32, 101, 137, 12, 151, 125}, [{4, 5, 6, 9, 1... \n","2010 ({66, 130, 4, 106, 75, 124}, [{0, 1, 2, 3, 22,... \n","2020 ({129, 4, 102, 11, 87, 121}, [{0, 1, 2, 3, 148... \n","2026 ({0, 4, 38, 144, 19, 58}, [{128, 4, 5, 6, 12, ... \n","2023 ({128, 68, 15, 145, 83, 28}, [{160, 129, 66, 1... \n","2001 ({0, 162, 99, 130, 47, 56}, [{96, 65, 1, 0, 6,... \n","2018 ({0, 1, 163, 69, 139, 26}, [{1, 2, 131, 4, 5, ... \n","2007 ({128, 3, 7, 136, 145, 86}, [{0, 1, 2, 4, 5, 6... \n","2002 ({0, 4, 138, 52, 93}, [{4, 5, 6, 7, 12, 13, 14... \n","2009 ({128, 0, 69, 137, 140}, [{0, 1, 2, 3, 11, 22,... \n","2016 ({128, 1, 0, 5, 78, 112}, [{128, 130, 135, 136... \n","2006 ({67, 163, 135, 14, 57, 158}, [{0, 1, 2, 131, ... \n","2003 ({128, 131, 6, 24, 154, 156}, [{1, 2, 3, 5, 7,... \n","2008 ({106, 123, 78, 15, 58, 27}, [{0, 1, 2, 8, 19,... \n","2014 ({0, 129, 1, 4, 119}, [{0, 2, 3, 7, 22, 23, 26... \n","2021 ({163, 9, 11, 19, 116, 126}, [{0, 132, 133, 13... \n","2004 ({4, 8, 75, 44, 13, 95}, [{0, 1, 2, 3, 6, 17, ... \n","2011 ({65, 38, 7, 136, 11, 77}, [{128, 1, 2, 3, 0, ... \n","2005 ({160, 0, 4, 7, 53, 62}, [{0, 1, 2, 3, 132, 8,... \n","2012 ({19, 121, 155, 0}, [{128, 129, 130, 0, 133, 1... \n","2042 ({99, 6, 11, 142, 26, 126}, [{4, 5, 9, 138, 10... \n","2044 ({0, 129, 4, 14, 157, 62}, [{4, 5, 6, 7, 9, 10... \n","2013 ({6, 11, 46, 143, 16, 159}, [{0, 1, 2, 3, 140,... \n","2067 ({128, 0, 2, 70, 10, 82}, [{2, 3, 4, 5, 9, 146... \n","2062 ({162, 130, 7, 140, 15, 49}, [{4, 5, 6, 8, 12,... \n","2052 ({0, 129, 99, 143, 89, 155}, [{0, 1, 2, 3, 7, ... \n","2070 ({0, 129, 101, 70, 7}, [{0, 1, 2, 3, 22, 24, 2... \n","2068 ({162, 132, 4, 72, 12}, [{0, 12, 13, 26, 27, 2... \n","2035 ({162, 41, 14, 51, 24, 59}, [{4, 5, 6, 9, 10, ... \n","2030 ({128, 0, 132, 122, 63}, [{0, 5, 6, 11, 13, 15... \n","2036 ({0, 5, 40, 8, 156, 126}, [{4, 5, 102, 91, 108... \n","2033 ({130, 4, 136, 22, 155, 157}, [{0, 1, 2, 3, 6,... \n","2029 ({0, 4, 7, 56, 62}, [{0, 1, 2, 3, 140, 141, 23... \n","2038 ({160, 1, 7, 42, 157}, [{0, 132, 133, 134, 6, ... \n","2063 ({128, 0, 74, 12, 142}, [{0, 1, 2, 131, 3, 140... \n","2061 ({0, 129, 34, 7, 55}, [{0, 1, 2, 3, 4, 9, 10, ... \n","2059 ({0, 4, 38, 9, 153, 28}, [{4, 5, 6, 8, 12, 15,... \n","2040 ({8, 41, 16, 24, 154, 93}, [{4, 5, 6, 7, 146, ... \n","2056 ({128, 0, 68, 14, 93}, [{0, 1, 131, 132, 134, ... \n","2048 ({72, 45, 48, 121, 90, 157, 62}, [{64, 0, 68, ... \n","2073 ({0, 130, 5, 101, 16}, [{128, 129, 4, 5, 9, 10... \n","2076 ({4, 7, 139, 152, 57}, [{0, 1, 2, 3, 136, 11, ... \n","2039 ({0, 4, 137, 90, 156}, [{128, 130, 5, 12, 13, ... \n","2051 ({129, 100, 76, 116, 23, 155}, [{128, 1, 2, 0,... \n","2049 ({64, 0, 36, 11, 156}, [{4, 5, 11, 12, 13, 15,... \n","2075 ({0, 33, 129, 143, 63}, [{0, 1, 2, 131, 132, 5... \n","2043 ({2, 133, 70, 78, 115}, [{4, 5, 6, 10, 20, 21,... \n","2069 ({128, 1, 0, 7, 81, 60}, [{0, 2, 131, 3, 6, 14... \n","2027 ({64, 1, 128, 15, 51}, [{0, 1, 130, 3, 2, 7, 1... \n","2074 ({128, 0, 66, 78, 28}, [{0, 1, 2, 3, 140, 18, ... \n","2058 ({0, 5, 70, 141, 126}, [{128, 1, 2, 3, 0, 6, 1... \n","2055 ({0, 129, 135, 142, 112, 154}, [{0, 1, 3, 7, 8... \n","2065 ({0, 130, 4, 41, 145, 89}, [{0, 131, 132, 134,... \n","2053 ({0, 3, 42, 60, 159}, [{128, 0, 132, 5, 134, 4... \n","2046 ({160, 3, 101, 12, 19}, [{0, 4, 5, 13, 18, 34,... \n","2072 ({0, 128, 8, 108, 155}, [{0, 1, 2, 3, 138, 140... \n","2034 ({0, 1, 3, 154, 126}, [{1, 4, 7, 9, 10, 142, 1... \n","2041 ({0, 162, 4, 14, 145}, [{129, 130, 5, 7, 12, 1... \n","2057 ({128, 131, 4, 8, 75, 24}, [{5, 7, 9, 10, 17, ... \n","2031 ({129, 131, 37, 6, 54, 155}, [{128, 130, 4, 13... \n","2066 ({64, 1, 133, 10, 24}, [{0, 1, 2, 3, 140, 141,... \n","2064 ({0, 129, 100, 43, 51}, [{0, 1, 2, 131, 132, 3... \n","2032 ({128, 0, 70, 7, 141, 118}, [{0, 1, 2, 3, 23, ... \n","2054 ({132, 100, 138, 12, 154, 123}, [{4, 5, 6, 9, ... \n","2071 ({0, 129, 4, 74, 151}, [{4, 5, 6, 7, 9, 10, 15... \n","2060 ({128, 0, 163, 4, 38, 153}, [{0, 1, 2, 131, 13... \n","2028 ({160, 129, 0, 1, 54}, [{1, 3, 5, 7, 10, 11, 1... \n","2045 ({0, 97, 12, 94, 63}, [{128, 5, 134, 6, 12, 13... \n","2050 ({2, 132, 9, 61, 126}, [{1, 5, 6, 12, 18, 22, ... \n","2047 ({0, 163, 5, 138, 60}, [{1, 3, 4, 7, 12, 147, ... \n","2037 ({0, 162, 13, 46, 126}, [{0, 1, 2, 3, 7, 8, 10... \n","2099 ({0, 1, 105, 114, 19}, [{128, 0, 130, 2, 11, 1... \n","2114 ({0, 130, 5, 24, 153}, [{5, 7, 9, 10, 145, 146... \n","2108 ({0, 163, 9, 138, 111}, [{128, 129, 4, 5, 6, 1... \n","2104 ({2, 132, 136, 111, 52, 31}, [{1, 4, 5, 6, 12,... \n","2078 ({128, 66, 7, 44, 141, 56}, [{0, 1, 2, 131, 3,... \n","2101 ({64, 128, 1, 38, 137, 16}, [{0, 2, 3, 140, 14... \n","2110 ({0, 98, 130, 101, 139}, [{128, 0, 4, 5, 10, 1... \n","2081 ({0, 4, 43, 143, 79}, [{4, 5, 6, 9, 12, 13, 14... \n","2087 ({0, 1, 130, 141, 114}, [{1, 2, 3, 10, 16, 22,... \n","2121 ({0, 129, 5, 70, 138, 59}, [{0, 1, 7, 136, 8, ... \n","2092 ({0, 129, 5, 39, 121, 154}, [{0, 1, 2, 3, 132,... \n","2079 ({0, 130, 132, 20, 119}, [{161, 34, 6, 8, 42, ... \n","2080 ({0, 161, 99, 7, 149, 57}, [{5, 7, 8, 9, 10, 1... \n","2113 ({0, 129, 4, 72, 142, 119}, [{4, 5, 6, 9, 10, ... \n","2094 ({128, 0, 14, 51, 59}, [{1, 12, 14, 16, 17, 22... \n","2112 ({0, 129, 7, 58, 62}, [{4, 5, 7, 9, 10, 11, 12... \n","2091 ({161, 8, 11, 108, 23, 155}, [{0, 1, 2, 131, 3... \n","2090 ({97, 135, 15, 113, 22, 151}, [{128, 1, 130, 3... \n","2105 ({97, 130, 3, 100, 6, 135}, [{0, 129, 2, 1, 8,... \n","2102 ({0, 129, 104, 137, 79}, [{4, 5, 7, 9, 10, 11,... \n","2088 ({0, 8, 41, 14, 146}, [{5, 12, 13, 14, 15, 16,... \n","2109 ({0, 101, 7, 11, 150, 55}, [{7, 138, 140, 141,... \n","2084 ({0, 131, 36, 10, 51}, [{7, 9, 138, 146, 19, 1... \n","2098 ({153, 2, 6, 121, 31}, [{0, 97, 98, 1, 90, 7, ... \n","2118 ({128, 0, 66, 29, 94}, [{4, 5, 6, 7, 137, 9, 1... \n","2119 ({131, 14, 148, 152, 58}, [{0, 2, 138, 140, 14... \n","2115 ({0, 128, 6, 107, 19}, [{0, 1, 2, 3, 139, 140,... \n","2086 ({130, 14, 20, 22, 56, 31}, [{1, 4, 8, 21, 23,... \n","2124 ({4, 133, 71, 85, 156}, [{0, 1, 2, 3, 22, 23, ... \n","2100 ({0, 4, 7, 149, 95}, [{128, 131, 4, 5, 6, 10, ... \n","2117 ({0, 139, 18, 90, 123}, [{128, 129, 130, 3, 13... \n","2103 ({1, 66, 163, 4, 11, 139}, [{134, 7, 8, 9, 146... \n","2125 ({0, 163, 5, 22, 89}, [{0, 1, 2, 3, 9, 10, 16,... \n","2085 ({101, 7, 135, 41, 157}, [{1, 130, 4, 5, 6, 9,... \n","2120 ({68, 135, 137, 105, 75, 23}, [{128, 129, 130,... \n","2097 ({97, 4, 8, 12, 142, 151}, [{128, 129, 130, 13... \n","2089 ({0, 130, 5, 38, 8, 139}, [{128, 5, 11, 12, 13... \n","2107 ({0, 129, 7, 40, 157, 93}, [{4, 6, 10, 12, 14,... \n","2106 ({0, 4, 136, 78, 48}, [{4, 5, 6, 11, 16, 17, 2... \n","2095 ({96, 128, 160, 107, 11, 22}, [{4, 5, 6, 18, 1... \n","2093 ({0, 4, 138, 153, 154}, [{0, 1, 2, 3, 139, 140... \n","2083 ({0, 4, 81, 24, 155}, [{32, 1, 2, 3, 0, 37, 72... \n","2122 ({128, 161, 0, 131, 148, 59}, [{4, 5, 15, 17, ... \n","2111 ({0, 99, 4, 142, 17}, [{128, 1, 130, 0, 133, 1... \n","2082 ({0, 67, 133, 7, 141, 29}, [{128, 97, 34, 35, ... \n","2126 ({0, 130, 7, 108, 151, 156}, [{4, 6, 8, 9, 10,... \n","2116 ({0, 130, 132, 7, 71}, [{7, 11, 16, 19, 21, 27... \n","2096 ({0, 130, 7, 137, 24}, [{0, 1, 2, 131, 132, 5,... \n","2077 ({0, 129, 35, 70, 119}, [{128, 0, 4, 5, 6, 28,... \n","2123 ({129, 6, 135, 11, 159}, [{0, 1, 2, 3, 4, 5, 7... \n","2148 ({0, 133, 37, 138, 15, 158}, [{4, 5, 6, 13, 16... \n","2155 ({0, 129, 163, 113, 63}, [{0, 1, 2, 3, 23, 25,... \n","2130 ({0, 133, 138, 16, 145}, [{0, 1, 2, 3, 6, 137,... \n","2171 ({65, 99, 139, 53, 25}, [{0, 129, 2, 3, 4, 1, ... \n","2129 ({133, 107, 18, 154, 61}, [{0, 1, 2, 3, 9, 148... \n","2151 ({128, 1, 131, 140, 153}, [{129, 4, 5, 6, 9, 1... \n","2145 ({160, 0, 5, 75, 14}, [{133, 6, 5, 137, 13, 16... \n","2142 ({0, 1, 4, 49, 148}, [{1, 8, 9, 10, 12, 13, 14... \n","2156 ({0, 4, 102, 90, 155}, [{130, 4, 5, 6, 9, 11, ... \n","2143 ({128, 0, 8, 20, 156, 61}, [{0, 3, 7, 137, 144... \n","2167 ({0, 129, 135, 137, 108, 150}, [{128, 4, 5, 12... \n","2144 ({97, 100, 11, 81, 59}, [{128, 129, 2, 3, 1, 1... \n","2147 ({130, 4, 136, 53, 152, 91}, [{0, 1, 2, 3, 6, ... \n","2152 ({161, 129, 2, 6, 155, 126}, [{0, 1, 3, 4, 5, ... \n","2163 ({0, 99, 4, 62, 31}, [{0, 1, 2, 3, 24, 25, 27,... \n","2138 ({160, 0, 128, 14, 19}, [{0, 1, 2, 131, 132, 1... \n","2159 ({0, 3, 163, 5, 135, 22}, [{3, 4, 6, 7, 8, 14,... \n","2158 ({0, 138, 12, 154, 94}, [{0, 1, 2, 3, 6, 8, 10... \n","2134 ({128, 0, 35, 18, 19}, [{4, 5, 6, 8, 9, 10, 13... \n","2169 ({128, 2, 9, 141, 94}, [{4, 5, 6, 7, 11, 12, 1... \n","2136 ({0, 100, 4, 139, 12, 156}, [{4, 5, 6, 10, 11,... \n","2137 ({160, 1, 128, 7, 59}, [{4, 5, 12, 13, 146, 14... \n","2166 ({128, 0, 67, 5, 139, 47}, [{128, 129, 130, 11... \n","2170 ({128, 0, 163, 137, 111, 145}, [{4, 5, 6, 7, 1... \n","2128 ({0, 132, 69, 9, 49}, [{0, 1, 2, 13, 15, 16, 1... \n","2149 ({17, 82, 50, 151, 157}, [{0, 1, 2, 3, 7, 8, 9... \n","2172 ({135, 42, 10, 141, 53}, [{0, 4, 133, 134, 7, ... \n","2168 ({0, 4, 133, 70, 39, 150}, [{129, 4, 5, 6, 11,... \n","2160 ({0, 137, 139, 81, 56}, [{0, 1, 2, 3, 7, 8, 9,... \n","2154 ({128, 163, 8, 10, 15, 60}, [{0, 1, 2, 131, 3,... \n","2161 ({99, 6, 15, 144, 22}, [{0, 1, 2, 3, 145, 18, ... \n","2140 ({0, 162, 6, 143}, [{128, 1, 2, 3, 4, 5, 0, 13... \n","2164 ({0, 1, 4, 14, 20, 127}, [{130, 4, 5, 12, 16, ... \n","2165 ({1, 101, 134, 24, 125}, [{0, 1, 2, 3, 140, 14... \n","2146 ({0, 98, 4, 135, 141, 158}, [{128, 1, 2, 3, 0,... \n","2150 ({128, 0, 4, 47, 157}, [{0, 1, 2, 3, 9, 22, 23... \n","2141 ({0, 4, 100, 13, 154}, [{4, 5, 6, 9, 16, 17, 2... \n","2131 ({131, 69, 8, 43, 15, 157}, [{0, 1, 2, 3, 18, ... \n","2135 ({1, 130, 131, 42, 152}, [{128, 129, 4, 5, 9, ... \n","2127 ({161, 135, 12, 48, 29}, [{0, 1, 2, 3, 4, 7, 8... \n","2132 ({0, 130, 131, 138, 19}, [{130, 7, 8, 11, 12, ... \n","2162 ({131, 36, 5, 7, 142, 28}, [{13, 17, 146, 148,... \n","2157 ({0, 1, 163, 16, 124}, [{160, 161, 162, 3, 1, ... \n","2139 ({128, 161, 135, 39, 9, 56}, [{4, 5, 6, 7, 144... \n","2133 ({100, 18, 122, 156, 30}, [{0, 129, 130, 3, 2,... \n","2153 ({136, 8, 108, 143, 154}, [{0, 1, 130, 3, 2, 1... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","2019 39.0 \n","2024 31.0 \n","2022 32.0 \n","2015 30.0 \n","2025 26.0 \n","2017 29.0 \n","2010 32.0 \n","2020 29.0 \n","2026 23.0 \n","2023 26.0 \n","2001 25.0 \n","2018 37.0 \n","2007 32.0 \n","2002 44.0 \n","2009 37.0 \n","2016 25.0 \n","2006 38.0 \n","2003 28.0 \n","2008 37.0 \n","2014 37.0 \n","2021 24.0 \n","2004 27.0 \n","2011 31.0 \n","2005 30.0 \n","2012 66.0 \n","2042 30.0 \n","2044 38.0 \n","2013 28.0 \n","2067 24.0 \n","2062 25.0 \n","2052 29.0 \n","2070 26.0 \n","2068 37.0 \n","2035 30.0 \n","2030 50.0 \n","2036 29.0 \n","2033 41.0 \n","2029 29.0 \n","2038 56.0 \n","2063 33.0 \n","2061 32.0 \n","2059 25.0 \n","2040 34.0 \n","2056 36.0 \n","2048 33.0 \n","2073 39.0 \n","2076 38.0 \n","2039 31.0 \n","2051 39.0 \n","2049 32.0 \n","2075 38.0 \n","2043 29.0 \n","2069 40.0 \n","2027 27.0 \n","2074 24.0 \n","2058 31.0 \n","2055 39.0 \n","2065 36.0 \n","2053 30.0 \n","2046 42.0 \n","2072 34.0 \n","2034 47.0 \n","2041 58.0 \n","2057 30.0 \n","2031 33.0 \n","2066 37.0 \n","2064 34.0 \n","2032 25.0 \n","2054 37.0 \n","2071 50.0 \n","2060 23.0 \n","2028 35.0 \n","2045 30.0 \n","2050 29.0 \n","2047 35.0 \n","2037 27.0 \n","2099 31.0 \n","2114 34.0 \n","2108 29.0 \n","2104 26.0 \n","2078 30.0 \n","2101 29.0 \n","2110 35.0 \n","2081 29.0 \n","2087 45.0 \n","2121 22.0 \n","2092 44.0 \n","2079 31.0 \n","2080 24.0 \n","2113 27.0 \n","2094 30.0 \n","2112 45.0 \n","2091 29.0 \n","2090 29.0 \n","2105 41.0 \n","2102 45.0 \n","2088 30.0 \n","2109 23.0 \n","2084 28.0 \n","2098 26.0 \n","2118 45.0 \n","2119 33.0 \n","2115 29.0 \n","2086 27.0 \n","2124 39.0 \n","2100 35.0 \n","2117 23.0 \n","2103 28.0 \n","2125 57.0 \n","2085 51.0 \n","2120 36.0 \n","2097 30.0 \n","2089 43.0 \n","2107 27.0 \n","2106 31.0 \n","2095 26.0 \n","2093 36.0 \n","2083 32.0 \n","2122 26.0 \n","2111 44.0 \n","2082 29.0 \n","2126 48.0 \n","2116 34.0 \n","2096 39.0 \n","2077 36.0 \n","2123 71.0 \n","2148 41.0 \n","2155 27.0 \n","2130 33.0 \n","2171 71.0 \n","2129 44.0 \n","2151 38.0 \n","2145 35.0 \n","2142 39.0 \n","2156 37.0 \n","2143 33.0 \n","2167 27.0 \n","2144 38.0 \n","2147 25.0 \n","2152 26.0 \n","2163 24.0 \n","2138 44.0 \n","2159 39.0 \n","2158 61.0 \n","2134 50.0 \n","2169 28.0 \n","2136 43.0 \n","2137 29.0 \n","2166 30.0 \n","2170 32.0 \n","2128 27.0 \n","2149 43.0 \n","2172 49.0 \n","2168 31.0 \n","2160 33.0 \n","2154 50.0 \n","2161 39.0 \n","2140 68.0 \n","2164 28.0 \n","2165 41.0 \n","2146 29.0 \n","2150 42.0 \n","2141 24.0 \n","2131 28.0 \n","2135 33.0 \n","2127 47.0 \n","2132 37.0 \n","2162 25.0 \n","2157 29.0 \n","2139 36.0 \n","2133 37.0 \n","2153 40.0 \n","\n"," Approximation and Heuristics Average Clustering \\\n","2019 0.693 \n","2024 0.644 \n","2022 0.659 \n","2015 0.649 \n","2025 0.639 \n","2017 0.652 \n","2010 0.675 \n","2020 0.651 \n","2026 0.608 \n","2023 0.620 \n","2001 0.627 \n","2018 0.650 \n","2007 0.623 \n","2002 0.694 \n","2009 0.675 \n","2016 0.628 \n","2006 0.682 \n","2003 0.654 \n","2008 0.697 \n","2014 0.667 \n","2021 0.645 \n","2004 0.623 \n","2011 0.660 \n","2005 0.636 \n","2012 0.801 \n","2042 0.659 \n","2044 0.652 \n","2013 0.624 \n","2067 0.670 \n","2062 0.633 \n","2052 0.651 \n","2070 0.635 \n","2068 0.698 \n","2035 0.646 \n","2030 0.763 \n","2036 0.668 \n","2033 0.738 \n","2029 0.648 \n","2038 0.738 \n","2063 0.697 \n","2061 0.663 \n","2059 0.605 \n","2040 0.645 \n","2056 0.657 \n","2048 0.653 \n","2073 0.695 \n","2076 0.683 \n","2039 0.653 \n","2051 0.696 \n","2049 0.672 \n","2075 0.731 \n","2043 0.647 \n","2069 0.653 \n","2027 0.663 \n","2074 0.648 \n","2058 0.685 \n","2055 0.657 \n","2065 0.669 \n","2053 0.643 \n","2046 0.738 \n","2072 0.664 \n","2034 0.747 \n","2041 0.742 \n","2057 0.678 \n","2031 0.637 \n","2066 0.646 \n","2064 0.702 \n","2032 0.645 \n","2054 0.673 \n","2071 0.719 \n","2060 0.636 \n","2028 0.716 \n","2045 0.660 \n","2050 0.626 \n","2047 0.673 \n","2037 0.627 \n","2099 0.639 \n","2114 0.686 \n","2108 0.666 \n","2104 0.591 \n","2078 0.690 \n","2101 0.646 \n","2110 0.668 \n","2081 0.648 \n","2087 0.757 \n","2121 0.613 \n","2092 0.679 \n","2079 0.630 \n","2080 0.613 \n","2113 0.613 \n","2094 0.649 \n","2112 0.709 \n","2091 0.653 \n","2090 0.684 \n","2105 0.708 \n","2102 0.727 \n","2088 0.662 \n","2109 0.579 \n","2084 0.617 \n","2098 0.651 \n","2118 0.686 \n","2119 0.696 \n","2115 0.635 \n","2086 0.654 \n","2124 0.696 \n","2100 0.652 \n","2117 0.632 \n","2103 0.596 \n","2125 0.797 \n","2085 0.748 \n","2120 0.651 \n","2097 0.653 \n","2089 0.709 \n","2107 0.636 \n","2106 0.647 \n","2095 0.636 \n","2093 0.684 \n","2083 0.627 \n","2122 0.646 \n","2111 0.674 \n","2082 0.644 \n","2126 0.706 \n","2116 0.674 \n","2096 0.696 \n","2077 0.667 \n","2123 0.803 \n","2148 0.748 \n","2155 0.716 \n","2130 0.727 \n","2171 0.803 \n","2129 0.765 \n","2151 0.714 \n","2145 0.665 \n","2142 0.685 \n","2156 0.697 \n","2143 0.668 \n","2167 0.641 \n","2144 0.701 \n","2147 0.628 \n","2152 0.688 \n","2163 0.634 \n","2138 0.707 \n","2159 0.647 \n","2158 0.756 \n","2134 0.755 \n","2169 0.709 \n","2136 0.664 \n","2137 0.636 \n","2166 0.669 \n","2170 0.620 \n","2128 0.654 \n","2149 0.717 \n","2172 0.699 \n","2168 0.654 \n","2160 0.664 \n","2154 0.748 \n","2161 0.738 \n","2140 0.839 \n","2164 0.621 \n","2165 0.699 \n","2146 0.648 \n","2150 0.702 \n","2141 0.633 \n","2131 0.645 \n","2135 0.705 \n","2127 0.733 \n","2132 0.708 \n","2162 0.644 \n","2157 0.679 \n","2139 0.701 \n","2133 0.655 \n","2153 0.710 \n","\n"," Approximation and Heuristics Diameter \\\n","2019 2.0 \n","2024 2.0 \n","2022 2.0 \n","2015 2.0 \n","2025 2.0 \n","2017 2.0 \n","2010 2.0 \n","2020 2.0 \n","2026 2.0 \n","2023 2.0 \n","2001 2.0 \n","2018 2.0 \n","2007 2.0 \n","2002 2.0 \n","2009 2.0 \n","2016 2.0 \n","2006 2.0 \n","2003 2.0 \n","2008 2.0 \n","2014 2.0 \n","2021 2.0 \n","2004 2.0 \n","2011 2.0 \n","2005 2.0 \n","2012 2.0 \n","2042 2.0 \n","2044 2.0 \n","2013 2.0 \n","2067 2.0 \n","2062 2.0 \n","2052 2.0 \n","2070 2.0 \n","2068 2.0 \n","2035 2.0 \n","2030 2.0 \n","2036 2.0 \n","2033 2.0 \n","2029 2.0 \n","2038 2.0 \n","2063 2.0 \n","2061 2.0 \n","2059 2.0 \n","2040 2.0 \n","2056 2.0 \n","2048 2.0 \n","2073 2.0 \n","2076 2.0 \n","2039 2.0 \n","2051 2.0 \n","2049 2.0 \n","2075 2.0 \n","2043 2.0 \n","2069 2.0 \n","2027 2.0 \n","2074 2.0 \n","2058 2.0 \n","2055 2.0 \n","2065 2.0 \n","2053 2.0 \n","2046 2.0 \n","2072 2.0 \n","2034 2.0 \n","2041 2.0 \n","2057 2.0 \n","2031 2.0 \n","2066 2.0 \n","2064 2.0 \n","2032 2.0 \n","2054 2.0 \n","2071 2.0 \n","2060 2.0 \n","2028 2.0 \n","2045 2.0 \n","2050 2.0 \n","2047 2.0 \n","2037 2.0 \n","2099 2.0 \n","2114 2.0 \n","2108 2.0 \n","2104 2.0 \n","2078 2.0 \n","2101 2.0 \n","2110 2.0 \n","2081 2.0 \n","2087 2.0 \n","2121 2.0 \n","2092 2.0 \n","2079 2.0 \n","2080 2.0 \n","2113 2.0 \n","2094 2.0 \n","2112 2.0 \n","2091 2.0 \n","2090 2.0 \n","2105 2.0 \n","2102 2.0 \n","2088 2.0 \n","2109 2.0 \n","2084 2.0 \n","2098 2.0 \n","2118 2.0 \n","2119 2.0 \n","2115 2.0 \n","2086 2.0 \n","2124 2.0 \n","2100 2.0 \n","2117 2.0 \n","2103 2.0 \n","2125 2.0 \n","2085 2.0 \n","2120 2.0 \n","2097 2.0 \n","2089 2.0 \n","2107 2.0 \n","2106 2.0 \n","2095 2.0 \n","2093 2.0 \n","2083 2.0 \n","2122 2.0 \n","2111 2.0 \n","2082 2.0 \n","2126 2.0 \n","2116 2.0 \n","2096 2.0 \n","2077 2.0 \n","2123 2.0 \n","2148 2.0 \n","2155 2.0 \n","2130 2.0 \n","2171 2.0 \n","2129 2.0 \n","2151 2.0 \n","2145 2.0 \n","2142 2.0 \n","2156 2.0 \n","2143 2.0 \n","2167 2.0 \n","2144 2.0 \n","2147 2.0 \n","2152 2.0 \n","2163 2.0 \n","2138 2.0 \n","2159 2.0 \n","2158 2.0 \n","2134 2.0 \n","2169 2.0 \n","2136 2.0 \n","2137 2.0 \n","2166 2.0 \n","2170 2.0 \n","2128 2.0 \n","2149 2.0 \n","2172 2.0 \n","2168 2.0 \n","2160 2.0 \n","2154 2.0 \n","2161 2.0 \n","2140 2.0 \n","2164 2.0 \n","2165 2.0 \n","2146 2.0 \n","2150 2.0 \n","2141 2.0 \n","2131 2.0 \n","2135 2.0 \n","2127 2.0 \n","2132 2.0 \n","2162 2.0 \n","2157 2.0 \n","2139 2.0 \n","2133 2.0 \n","2153 2.0 \n","\n"," Approximation and Heuristics Min Edge Dominating Set \\\n","2019 {(54, 55), (100, 101), (40, 41), (72, 73), (18... \n","2024 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2022 {(54, 55), (86, 87), (154, 156), (40, 41), (72... \n","2015 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2025 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2017 {(54, 55), (100, 101), (125, 126), (154, 156),... \n","2010 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2020 {(54, 55), (86, 87), (92, 93), (40, 41), (72, ... \n","2026 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2023 {(54, 55), (86, 87), (92, 93), (156, 157), (72... \n","2001 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2018 {(54, 55), (86, 87), (156, 157), (72, 73), (34... \n","2007 {(54, 55), (86, 87), (92, 93), (125, 126), (15... \n","2002 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2009 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2016 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2006 {(6, 9), (54, 55), (86, 87), (92, 93), (100, 1... \n","2003 {(14, 17), (54, 55), (86, 87), (156, 157), (40... \n","2008 {(6, 9), (54, 55), (86, 87), (92, 93), (100, 1... \n","2014 {(54, 55), (86, 87), (7, 12), (156, 157), (17,... \n","2021 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2004 {(6, 9), (65, 67), (54, 55), (82, 86), (156, 1... \n","2011 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2005 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2012 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2042 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2044 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2013 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2067 {(65, 67), (86, 87), (156, 157), (40, 41), (72... \n","2062 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2052 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2070 {(54, 55), (156, 157), (40, 41), (72, 73), (18... \n","2068 {(86, 87), (125, 126), (156, 157), (40, 41), (... \n","2035 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2030 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2036 {(65, 67), (54, 55), (125, 126), (156, 157), (... \n","2033 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2029 {(54, 55), (62, 64), (92, 93), (125, 126), (15... \n","2038 {(54, 55), (136, 141), (125, 126), (154, 156),... \n","2063 {(54, 55), (92, 93), (125, 126), (86, 90), (15... \n","2061 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2059 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2040 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2056 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2048 {(65, 67), (54, 55), (86, 87), (156, 157), (40... \n","2073 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2076 {(54, 55), (86, 87), (100, 101), (40, 41), (72... \n","2039 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2051 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2049 {(134, 137), (54, 55), (100, 101), (156, 157),... \n","2075 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2043 {(54, 55), (86, 87), (92, 93), (100, 101), (21... \n","2069 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2027 {(54, 55), (156, 157), (40, 41), (72, 73), (18... \n","2074 {(54, 55), (86, 87), (136, 141), (92, 93), (15... \n","2058 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2055 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2065 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2053 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2046 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2072 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2034 {(54, 55), (100, 101), (125, 126), (156, 157),... \n","2041 {(54, 55), (86, 87), (136, 141), (100, 101), (... \n","2057 {(54, 55), (86, 87), (10, 17), (92, 93), (100,... \n","2031 {(54, 55), (92, 93), (40, 41), (72, 73), (18, ... \n","2066 {(134, 137), (54, 55), (92, 93), (125, 126), (... \n","2064 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2032 {(6, 9), (54, 55), (86, 87), (92, 93), (125, 1... \n","2054 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2071 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2060 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2028 {(134, 137), (54, 55), (86, 87), (40, 41), (72... \n","2045 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2050 {(98, 102), (54, 55), (86, 87), (92, 93), (125... \n","2047 {(134, 137), (54, 55), (156, 157), (40, 41), (... \n","2037 {(54, 55), (100, 101), (125, 126), (40, 41), (... \n","2099 {(54, 55), (86, 87), (21, 28), (40, 41), (72, ... \n","2114 {(54, 55), (92, 93), (154, 156), (40, 41), (72... \n","2108 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2104 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2078 {(6, 9), (54, 55), (86, 87), (92, 93), (125, 1... \n","2101 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2110 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2081 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2087 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2121 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2092 {(54, 55), (92, 93), (156, 157), (40, 41), (72... \n","2079 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2080 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2113 {(54, 55), (154, 156), (40, 41), (72, 73), (18... \n","2094 {(6, 9), (54, 55), (86, 87), (125, 126), (40, ... \n","2112 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2091 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2090 {(6, 9), (98, 102), (54, 55), (86, 87), (156, ... \n","2105 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2102 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2088 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2109 {(98, 102), (54, 55), (86, 87), (156, 157), (4... \n","2084 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2098 {(54, 55), (86, 87), (100, 101), (40, 41), (72... \n","2118 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2119 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2115 {(54, 55), (86, 87), (156, 157), (95, 101), (4... \n","2086 {(54, 55), (86, 87), (100, 101), (26, 28), (15... \n","2124 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2100 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2117 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2103 {(134, 137), (54, 55), (86, 87), (92, 93), (12... \n","2125 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2085 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2120 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2097 {(134, 137), (54, 55), (86, 87), (156, 157), (... \n","2089 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2107 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2106 {(6, 9), (54, 55), (100, 101), (125, 126), (15... \n","2095 {(82, 86), (54, 55), (92, 93), (156, 157), (40... \n","2093 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2083 {(134, 137), (54, 55), (156, 157), (72, 73), (... \n","2122 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2111 {(134, 137), (54, 55), (86, 87), (125, 126), (... \n","2082 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2126 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2116 {(54, 55), (86, 87), (125, 126), (154, 156), (... \n","2096 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2077 {(98, 102), (54, 55), (86, 87), (10, 17), (156... \n","2123 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2148 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2155 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2130 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2171 {(54, 55), (86, 87), (92, 93), (156, 157), (72... \n","2129 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2151 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2145 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2142 {(54, 55), (125, 126), (86, 90), (154, 156), (... \n","2156 {(6, 9), (54, 55), (86, 87), (92, 93), (40, 41... \n","2143 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2167 {(54, 55), (86, 87), (156, 157), (17, 20), (40... \n","2144 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2147 {(98, 102), (54, 55), (86, 87), (154, 156), (4... \n","2152 {(98, 102), (54, 55), (86, 87), (156, 157), (4... \n","2163 {(82, 86), (54, 55), (92, 93), (100, 101), (15... \n","2138 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2159 {(86, 87), (154, 156), (40, 41), (72, 73), (18... \n","2158 {(54, 55), (86, 87), (156, 157), (26, 28), (40... \n","2134 {(86, 87), (156, 157), (40, 41), (72, 73), (34... \n","2169 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2136 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2137 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2166 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2170 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2128 {(54, 55), (100, 101), (125, 126), (156, 157),... \n","2149 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2172 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2168 {(54, 55), (86, 87), (10, 17), (100, 101), (15... \n","2160 {(86, 87), (92, 93), (100, 101), (156, 157), (... \n","2154 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2161 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2140 {(6, 9), (54, 55), (86, 87), (92, 93), (156, 1... \n","2164 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2165 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2146 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2150 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2141 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2131 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2135 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2127 {(54, 55), (86, 87), (40, 41), (72, 73), (34, ... \n","2132 {(134, 137), (54, 55), (100, 101), (156, 157),... \n","2162 {(6, 9), (54, 55), (86, 87), (10, 17), (100, 1... \n","2157 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2139 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2133 {(86, 87), (100, 101), (156, 157), (40, 41), (... \n","2153 {(54, 55), (92, 93), (156, 157), (40, 41), (72... \n","\n"," Approximation and Heuristics Min Wt Dominating Set \\\n","2019 {2, 136, 14, 16, 20, 21, 22, 26, 27, 28, 29, 3... \n","2024 {96, 98, 101, 102, 133, 139, 144, 117, 91, 62,... \n","2022 {3, 131, 135, 136, 144, 24, 32, 33, 38, 45, 46... \n","2015 {32, 162, 163, 100, 145, 149, 150, 151, 152, 5... \n","2025 {99, 4, 41, 137, 43, 44, 14, 47, 22, 152} \n","2017 {4, 146, 147, 150, 27, 30, 161, 162, 163, 35, ... \n","2010 {130, 4, 5, 11, 12, 140, 143, 16, 145, 157, 16... \n","2020 {130, 37, 103, 43, 148, 149, 150, 151} \n","2026 {101, 137, 114, 148, 151, 157, 30} \n","2023 {34, 35, 36, 11, 76, 12, 111, 115, 84, 116, 86... \n","2001 {106, 44, 46, 48, 146, 50, 51, 85, 60, 30} \n","2018 {96, 132, 101, 133, 134, 102, 137, 42, 144, 49... \n","2007 {37, 9, 10, 46, 48, 50, 51, 116, 56, 62} \n","2002 {96, 130, 132, 101, 102, 70, 133, 107, 13, 46,... \n","2009 {97, 100, 102, 70, 104, 9, 40, 75, 106, 42, 13... \n","2016 {131, 36, 133, 123, 108, 91, 124} \n","2006 {152, 24, 117, 151} \n","2003 {129, 46, 110, 49, 50, 51, 147, 54, 56, 28, 30... \n","2008 {100, 136, 43, 108, 80, 144, 85, 152, 26, 92, ... \n","2014 {134, 135, 138, 46, 47} \n","2021 {135, 105, 10, 138, 107, 77, 46, 81, 59, 29, 31} \n","2004 {70, 71, 40, 73, 47, 144, 113, 83, 27, 28, 157... \n","2011 {161, 17, 148, 154, 95} \n","2005 {8, 107, 13, 145, 29, 17, 152, 60, 93, 95} \n","2012 {128, 133, 6, 8, 9, 12, 13, 20, 21, 32, 33, 35... \n","2042 {97, 129, 100, 133, 103, 7, 105, 78, 116, 53, ... \n","2044 {133, 134, 12, 144, 145, 18, 146, 147, 26, 154... \n","2013 {4, 100, 104, 106, 138, 116, 153} \n","2067 {162, 100, 136, 43, 110, 144, 146, 116, 52, 12... \n","2062 {160, 100, 101, 104, 48, 151, 152, 59, 157} \n","2052 {128, 7, 8, 10, 141, 144, 147, 149, 158, 30, 1... \n","2070 {161, 163, 58, 5, 46, 48, 49, 50, 51, 145, 146... \n","2068 {101, 139, 45, 112, 114, 86, 118, 151} \n","2035 {131, 132, 134, 135, 155, 46, 144, 146, 83, 30... \n","2030 {104, 9, 76, 77, 46, 28} \n","2036 {159, 33, 34, 101, 102, 155, 108, 14, 15, 145,... \n","2033 {32, 100, 27, 106, 46, 84, 55, 24, 91, 93} \n","2029 {128, 162, 58, 133, 132, 134, 27, 40, 42, 138,... \n","2038 {104, 106, 51, 103} \n","2063 {46, 50, 152, 92, 158} \n","2061 {2, 3, 133, 134, 9, 10, 13, 145, 147, 27, 33, ... \n","2059 {129, 134, 136, 73, 43, 76, 46, 47, 48, 50, 11... \n","2040 {99, 101, 133, 138, 143, 47, 144, 146, 19, 147... \n","2056 {160, 34, 35, 133, 134, 138, 75, 74, 145, 146,... \n","2048 {4, 118, 150, 152, 57, 91} \n","2073 {160, 66, 68, 70, 71, 104, 11, 46, 78, 48, 113... \n","2076 {42, 43, 140, 141, 148, 86, 54, 30, 159} \n","2039 {32, 33, 133, 103, 110, 46, 142, 144, 145, 114... \n","2051 {0, 40, 137, 8, 11, 44, 43, 46, 14, 144, 145, ... \n","2049 {100, 133, 134, 101, 40, 10, 77, 47, 49, 29, 1... \n","2075 {128, 135, 136, 10, 145, 148, 26, 47, 90, 91, ... \n","2043 {134, 40, 28, 46, 47, 53, 58, 27, 156} \n","2069 {132, 133, 8, 9, 18, 151, 152, 153, 154, 159, ... \n","2027 {97, 103, 104, 107, 76, 13, 77, 80, 114, 147} \n","2074 {131, 75, 30, 92, 95, 127} \n","2058 {64, 128, 97, 6, 103, 104, 45, 46, 144, 145, 1... \n","2055 {99, 7, 106, 46, 47, 79, 145, 146, 52, 150, 12... \n","2065 {128, 131, 132, 134, 40, 82, 150, 59, 30, 127} \n","2053 {1, 99, 58, 6, 104, 48, 49, 51, 90} \n","2046 {2, 131, 133, 134, 136, 46, 146, 147, 115, 93} \n","2072 {5, 9, 142, 14, 22, 33, 35, 37, 42, 46, 62, 71... \n","2034 {128, 131, 132, 133, 134, 137, 13, 146, 19, 27... \n","2041 {96, 161, 131, 132, 100, 101, 99, 102, 38, 45,... \n","2057 {34, 4, 45, 46, 47, 112, 48, 110, 116, 56, 28,... \n","2031 {36, 14, 144, 81, 50, 18, 17, 146, 145, 19, 95} \n","2066 {130, 137, 138, 145, 147, 148, 150, 152, 153, ... \n","2064 {33, 131, 132, 133, 134, 7, 103, 78, 79, 145, ... \n","2032 {160, 1, 133, 134, 52, 54, 152, 30} \n","2054 {142, 144, 16, 145, 147, 19, 150, 152, 29, 30,... \n","2071 {134, 8, 91, 46, 47, 86, 94, 122, 59, 30, 127} \n","2060 {161, 34, 35, 100, 106, 44, 45, 47, 48, 81, 11... \n","2028 {1, 6, 7, 9, 10, 137, 13, 143, 147, 21, 29, 42... \n","2045 {128, 161, 162, 47, 114, 30} \n","2050 {4, 5, 12, 145, 18, 19, 150, 152, 155, 27, 30,... \n","2047 {101, 102, 107, 75, 144, 145, 51, 152} \n","2037 {103, 41, 143, 53, 27, 29, 62} \n","2099 {128, 130, 66, 133, 47, 52, 53, 55, 151, 26, 2... \n","2114 {128, 34, 133, 134, 136, 41, 48, 145, 144, 115... \n","2108 {128, 131, 132, 134, 136, 8, 18, 147, 25, 29, ... \n","2104 {1, 4, 5, 135, 10, 14, 145, 146, 159, 33, 43, ... \n","2078 {16, 156, 32, 161, 39, 40, 41, 43, 71, 84, 86,... \n","2101 {101, 141, 46, 111, 48, 49, 50, 84, 117, 149, ... \n","2110 {4, 133, 5, 9, 10, 146, 19, 20, 150, 154, 28, ... \n","2081 {33, 131, 146, 51, 116, 150, 57} \n","2087 {4, 5, 9, 10, 26, 27, 42, 43, 45, 47, 48, 50, ... \n","2121 {128, 102, 11, 144, 116, 85, 94} \n","2092 {1, 133, 134, 10, 16, 27, 46, 50, 51, 56, 57, ... \n","2079 {103, 48, 112, 146, 147, 49, 154, 159} \n","2080 {128, 130, 35, 36, 69, 102, 138, 46, 144, 16, ... \n","2113 {33, 162, 150, 31, 30, 159} \n","2094 {35, 101, 69, 40, 46, 112, 49, 52, 53, 117, 54... \n","2112 {37, 103, 8, 104, 76, 46, 47, 50, 51, 151, 155} \n","2091 {131, 133, 134, 42, 142, 143, 144, 145, 50, 93... \n","2090 {129, 132, 73, 107, 47, 145, 146, 53, 55, 92} \n","2105 {129, 99, 36, 133, 102, 72, 42, 79, 48, 84, 94} \n","2102 {128, 162, 133, 108, 86, 126, 127} \n","2088 {161, 37, 133, 38, 41, 42, 43, 46, 151, 26} \n","2109 {32, 129, 1, 26, 45, 46, 16, 56, 57, 126, 125,... \n","2084 {42, 43, 108, 12, 13, 142, 91, 44, 52, 26, 27,... \n","2098 {128, 129, 130, 2, 133, 136, 137, 138, 14, 143... \n","2118 {35, 5, 134, 37, 43, 44, 45, 110, 81, 82, 146,... \n","2119 {136, 12, 16, 18, 19, 21, 22, 26, 30, 31, 32, ... \n","2115 {101, 103, 8, 104, 12, 45, 146, 150, 54, 22, 1... \n","2086 {96, 34, 35, 36, 132, 101, 133, 27, 12, 45, 79... \n","2124 {128, 98, 134, 77, 48, 49, 116, 150, 58, 91} \n","2100 {98, 102, 27, 138, 77, 46, 47, 52, 53, 55, 56,... \n","2117 {5, 77, 82, 91, 158} \n","2103 {161, 34, 135, 40, 104, 76, 77, 143, 113, 114,... \n","2125 {9, 10, 13, 16, 18, 27, 28, 29, 34, 36, 37, 40... \n","2085 {1, 129, 67, 3, 103, 104, 74, 75, 11, 49, 50, ... \n","2120 {128, 4, 5, 134, 132, 144, 45, 65, 92, 103, 10... \n","2097 {0, 2, 133, 134, 41, 137, 46, 47, 80, 60, 144,... \n","2089 {128, 134, 137, 14, 151, 157, 33, 34, 35, 39, ... \n","2107 {128, 129, 70, 71, 104, 43, 77, 46, 92, 29, 51... \n","2106 {160, 130, 35, 100, 133, 134, 31, 47, 147, 116... \n","2095 {71, 13, 146, 86, 55, 57, 122, 27, 28} \n","2093 {129, 130, 12, 16, 17, 30, 33, 42, 43, 46, 47,... \n","2083 {128, 32, 33, 70, 138, 140, 111, 119, 24, 120,... \n","2122 {97, 98, 103, 104, 78, 47, 49, 50, 51, 117, 60... \n","2111 {161, 132, 103, 138, 107, 46, 15, 145, 147, 14... \n","2082 {128, 130, 10, 139, 138, 12, 13, 144, 145, 146... \n","2126 {129, 130, 131, 132, 133, 8, 13, 145, 19, 29, ... \n","2116 {96, 97, 134, 46, 113, 114, 156} \n","2096 {77, 142, 144, 145, 19, 52, 147, 85, 28} \n","2077 {0, 132, 100, 102, 36, 40, 46, 47, 48, 92, 18,... \n","2123 {0, 1, 2, 131, 4, 132, 134, 133, 135, 9, 10, 1... \n","2148 {129, 130, 98, 34, 104, 77, 46, 53} \n","2155 {160, 161, 98, 99, 97, 101, 100, 46, 124, 49, ... \n","2130 {101, 6, 102, 47, 144, 151, 56, 154, 28, 94} \n","2171 {0, 129, 128, 130, 3, 133, 2, 7, 6, 9, 10, 14,... \n","2129 {97, 162, 98, 100, 7, 80, 116, 120, 56, 123, 1... \n","2151 {32, 128, 8, 41, 15, 112, 17, 117, 118, 151, 92} \n","2145 {130, 98, 133, 134, 12, 127, 46, 144, 113, 50,... \n","2142 {103, 104, 135, 46, 27, 28, 30} \n","2156 {128, 9, 10, 19, 148, 149, 151, 24, 28, 29, 16... \n","2143 {128, 99, 35, 102, 134, 42, 80, 113, 114, 115,... \n","2167 {4, 138, 143, 17, 146, 24, 156, 157, 30, 162, ... \n","2144 {32, 129, 3, 36, 37, 38, 133, 104, 105, 76, 77... \n","2147 {128, 97, 6, 45, 110, 147, 119, 28, 157} \n","2152 {32, 33, 0, 36, 38, 71, 73, 43, 84, 52, 150, 2... \n","2163 {96, 102, 7, 74, 107, 13, 78, 46, 47, 119, 57,... \n","2138 {64, 5, 16, 145, 91} \n","2159 {162, 103, 105, 48, 145, 16, 147, 151, 28, 29,... \n","2158 {128, 0, 130, 3, 6, 135, 10, 20, 26, 28, 29, 1... \n","2134 {65, 131, 4, 70, 135, 72, 41, 40, 43, 111, 49,... \n","2169 {96, 97, 7, 48, 144, 122, 123, 124} \n","2136 {162, 101, 103, 48, 62, 30, 95} \n","2137 {128, 5, 135, 142, 150, 30, 34, 37, 41, 46, 47... \n","2166 {129, 97, 36, 4, 136, 42, 76, 45, 48, 113, 114... \n","2170 {33, 42, 43, 46, 49, 57, 26, 59, 28, 157, 127} \n","2128 {96, 128, 34, 35, 99, 133, 104, 9, 10, 76, 77,... \n","2149 {8, 9, 139, 76, 47, 53, 149} \n","2172 {128, 10, 144, 145, 146, 147, 47, 48, 49, 53, ... \n","2168 {40, 41, 43, 144, 145, 114, 49, 121, 26, 92, 95} \n","2160 {108, 12, 112, 50, 84, 54, 23, 152, 153, 63, 57} \n","2154 {33, 130, 131, 161, 133, 102, 35, 104, 9, 44, ... \n","2161 {153, 147, 111, 41} \n","2140 {130, 3, 9, 74, 77, 79, 88, 57} \n","2164 {36, 134, 103, 104, 27, 76, 77, 46, 12, 52, 11... \n","2165 {130, 132, 102, 135, 40, 75, 11, 108, 78, 79, ... \n","2146 {34, 143, 19, 148, 95} \n","2150 {5, 134, 133, 9, 28, 34, 36, 44, 46, 56, 57, 5... \n","2141 {163, 134, 40, 42, 54, 152, 56, 27, 28, 29} \n","2131 {130, 36, 137, 148, 53, 156} \n","2135 {34, 101, 5, 39, 41, 50, 147, 117, 30, 56, 156... \n","2127 {128, 2, 4, 9, 14, 148, 150, 152, 156, 43, 45,... \n","2132 {161, 162, 35, 36, 37, 6, 134, 27, 40, 113, 86... \n","2162 {130, 50, 149, 58, 91} \n","2157 {33, 44, 45, 28, 14, 51, 61, 55, 26, 92, 125, 63} \n","2139 {129, 130, 4, 5, 16, 147, 148, 152, 30, 161, 3... \n","2133 {128, 106, 48, 115, 27} \n","2153 {10, 75, 91, 45, 77, 86, 123, 124} \n","\n"," Approximation and Heuristics Maximal Matching \\\n","2019 {(54, 55), (100, 101), (40, 41), (72, 73), (18... \n","2024 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2022 {(54, 55), (86, 87), (154, 156), (40, 41), (72... \n","2015 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2025 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2017 {(54, 55), (100, 101), (125, 126), (154, 156),... \n","2010 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2020 {(54, 55), (86, 87), (92, 93), (40, 41), (72, ... \n","2026 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2023 {(54, 55), (86, 87), (92, 93), (156, 157), (72... \n","2001 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2018 {(54, 55), (86, 87), (156, 157), (72, 73), (34... \n","2007 {(54, 55), (86, 87), (92, 93), (125, 126), (15... \n","2002 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2009 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2016 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2006 {(6, 9), (54, 55), (86, 87), (92, 93), (100, 1... \n","2003 {(14, 17), (54, 55), (86, 87), (156, 157), (40... \n","2008 {(6, 9), (54, 55), (86, 87), (92, 93), (100, 1... \n","2014 {(54, 55), (86, 87), (7, 12), (156, 157), (17,... \n","2021 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2004 {(6, 9), (65, 67), (54, 55), (82, 86), (156, 1... \n","2011 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2005 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2012 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2042 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2044 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2013 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2067 {(65, 67), (86, 87), (156, 157), (40, 41), (72... \n","2062 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2052 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2070 {(54, 55), (156, 157), (40, 41), (72, 73), (18... \n","2068 {(86, 87), (125, 126), (156, 157), (40, 41), (... \n","2035 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2030 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2036 {(65, 67), (54, 55), (125, 126), (156, 157), (... \n","2033 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2029 {(54, 55), (62, 64), (92, 93), (125, 126), (15... \n","2038 {(54, 55), (136, 141), (125, 126), (154, 156),... \n","2063 {(54, 55), (92, 93), (125, 126), (86, 90), (15... \n","2061 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2059 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2040 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2056 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2048 {(65, 67), (54, 55), (86, 87), (156, 157), (40... \n","2073 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2076 {(54, 55), (86, 87), (100, 101), (40, 41), (72... \n","2039 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2051 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2049 {(134, 137), (54, 55), (100, 101), (156, 157),... \n","2075 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2043 {(54, 55), (86, 87), (92, 93), (100, 101), (21... \n","2069 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2027 {(54, 55), (156, 157), (40, 41), (72, 73), (18... \n","2074 {(54, 55), (86, 87), (136, 141), (92, 93), (15... \n","2058 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2055 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2065 {(54, 55), (92, 93), (125, 126), (156, 157), (... \n","2053 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2046 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2072 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2034 {(54, 55), (100, 101), (125, 126), (156, 157),... \n","2041 {(54, 55), (86, 87), (136, 141), (100, 101), (... \n","2057 {(54, 55), (86, 87), (10, 17), (92, 93), (100,... \n","2031 {(54, 55), (92, 93), (40, 41), (72, 73), (18, ... \n","2066 {(134, 137), (54, 55), (92, 93), (125, 126), (... \n","2064 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2032 {(6, 9), (54, 55), (86, 87), (92, 93), (125, 1... \n","2054 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2071 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2060 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2028 {(134, 137), (54, 55), (86, 87), (40, 41), (72... \n","2045 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2050 {(98, 102), (54, 55), (86, 87), (92, 93), (125... \n","2047 {(134, 137), (54, 55), (156, 157), (40, 41), (... \n","2037 {(54, 55), (100, 101), (125, 126), (40, 41), (... \n","2099 {(54, 55), (86, 87), (21, 28), (40, 41), (72, ... \n","2114 {(54, 55), (92, 93), (154, 156), (40, 41), (72... \n","2108 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2104 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2078 {(6, 9), (54, 55), (86, 87), (92, 93), (125, 1... \n","2101 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2110 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2081 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2087 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2121 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2092 {(54, 55), (92, 93), (156, 157), (40, 41), (72... \n","2079 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2080 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2113 {(54, 55), (154, 156), (40, 41), (72, 73), (18... \n","2094 {(6, 9), (54, 55), (86, 87), (125, 126), (40, ... \n","2112 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2091 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2090 {(6, 9), (98, 102), (54, 55), (86, 87), (156, ... \n","2105 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2102 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2088 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2109 {(98, 102), (54, 55), (86, 87), (156, 157), (4... \n","2084 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2098 {(54, 55), (86, 87), (100, 101), (40, 41), (72... \n","2118 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2119 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2115 {(54, 55), (86, 87), (156, 157), (95, 101), (4... \n","2086 {(54, 55), (86, 87), (100, 101), (26, 28), (15... \n","2124 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2100 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2117 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2103 {(134, 137), (54, 55), (86, 87), (92, 93), (12... \n","2125 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2085 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2120 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2097 {(134, 137), (54, 55), (86, 87), (156, 157), (... \n","2089 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2107 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2106 {(6, 9), (54, 55), (100, 101), (125, 126), (15... \n","2095 {(82, 86), (54, 55), (92, 93), (156, 157), (40... \n","2093 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2083 {(134, 137), (54, 55), (156, 157), (72, 73), (... \n","2122 {(54, 55), (86, 87), (100, 101), (154, 156), (... \n","2111 {(134, 137), (54, 55), (86, 87), (125, 126), (... \n","2082 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2126 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2116 {(54, 55), (86, 87), (125, 126), (154, 156), (... \n","2096 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2077 {(98, 102), (54, 55), (86, 87), (10, 17), (156... \n","2123 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2148 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2155 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2130 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2171 {(54, 55), (86, 87), (92, 93), (156, 157), (72... \n","2129 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2151 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2145 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2142 {(54, 55), (125, 126), (86, 90), (154, 156), (... \n","2156 {(6, 9), (54, 55), (86, 87), (92, 93), (40, 41... \n","2143 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2167 {(54, 55), (86, 87), (156, 157), (17, 20), (40... \n","2144 {(54, 55), (100, 101), (156, 157), (40, 41), (... \n","2147 {(98, 102), (54, 55), (86, 87), (154, 156), (4... \n","2152 {(98, 102), (54, 55), (86, 87), (156, 157), (4... \n","2163 {(82, 86), (54, 55), (92, 93), (100, 101), (15... \n","2138 {(6, 9), (54, 55), (86, 87), (156, 157), (40, ... \n","2159 {(86, 87), (154, 156), (40, 41), (72, 73), (18... \n","2158 {(54, 55), (86, 87), (156, 157), (26, 28), (40... \n","2134 {(86, 87), (156, 157), (40, 41), (72, 73), (34... \n","2169 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2136 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2137 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2166 {(54, 55), (86, 87), (100, 101), (156, 157), (... \n","2170 {(134, 137), (54, 55), (86, 87), (100, 101), (... \n","2128 {(54, 55), (100, 101), (125, 126), (156, 157),... \n","2149 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2172 {(54, 55), (86, 87), (92, 93), (156, 157), (40... \n","2168 {(54, 55), (86, 87), (10, 17), (100, 101), (15... \n","2160 {(86, 87), (92, 93), (100, 101), (156, 157), (... \n","2154 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","2161 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2140 {(6, 9), (54, 55), (86, 87), (92, 93), (156, 1... \n","2164 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2165 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2146 {(54, 55), (86, 87), (92, 93), (100, 101), (12... \n","2150 {(54, 55), (86, 87), (125, 126), (156, 157), (... \n","2141 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2131 {(54, 55), (86, 87), (156, 157), (40, 41), (72... \n","2135 {(54, 55), (86, 87), (40, 41), (72, 73), (18, ... \n","2127 {(54, 55), (86, 87), (40, 41), (72, 73), (34, ... \n","2132 {(134, 137), (54, 55), (100, 101), (156, 157),... \n","2162 {(6, 9), (54, 55), (86, 87), (10, 17), (100, 1... \n","2157 {(54, 55), (86, 87), (92, 93), (100, 101), (40... \n","2139 {(54, 55), (86, 87), (92, 93), (100, 101), (15... \n","2133 {(86, 87), (100, 101), (156, 157), (40, 41), (... \n","2153 {(54, 55), (92, 93), (156, 157), (40, 41), (72... \n","\n"," Approximation and Heuristics Ramsay \\\n","2019 ({4, 133, 6, 5, 16, 21, 44, 45, 50, 51, 57, 59... \n","2024 ({0, 1, 2, 131, 3, 6, 18, 25, 29, 32, 49, 53, ... \n","2022 ({0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 3... \n","2015 ({128, 129, 134, 12, 13, 14, 15, 16, 17, 22, 1... \n","2025 ({0, 1, 2, 3, 4, 14, 18, 19, 29, 32, 33, 36, 3... \n","2017 ({4, 5, 6, 9, 10, 18, 147, 20, 21, 30, 159, 34... \n","2010 ({0, 1, 2, 3, 22, 23, 25, 27, 32, 33, 38, 39, ... \n","2020 ({0, 1, 2, 3, 148, 149, 23, 28, 29, 47, 53, 54... \n","2026 ({128, 4, 5, 6, 12, 13, 16, 34, 35, 45, 48, 49... \n","2023 ({160, 129, 66, 130, 70, 7, 9, 74, 10, 140, 77... \n","2001 ({96, 65, 1, 0, 6, 111, 144, 145, 50, 83, 49, ... \n","2018 ({1, 2, 131, 4, 5, 6, 10, 144, 146, 19, 18, 21... \n","2007 ({0, 1, 2, 4, 5, 6, 19, 153, 46, 48, 52, 61, 6... \n","2002 ({4, 5, 6, 7, 12, 13, 145, 147, 21, 150, 161, ... \n","2009 ({0, 1, 2, 3, 11, 22, 29, 32, 33, 36, 37, 38, ... \n","2016 ({128, 130, 135, 136, 12, 13, 14, 15, 33, 34, ... \n","2006 ({0, 1, 2, 131, 132, 133, 3, 152, 156, 157, 32... \n","2003 ({1, 2, 3, 5, 7, 10, 144, 145, 19, 21, 155, 44... \n","2008 ({0, 1, 2, 8, 19, 23, 25, 26, 29, 32, 33, 36, ... \n","2014 ({0, 2, 3, 7, 22, 23, 26, 28, 33, 162, 36, 41,... \n","2021 ({0, 132, 133, 134, 135, 8, 7, 6, 5, 4, 143, 1... \n","2004 ({0, 1, 2, 3, 6, 17, 27, 28, 29, 50, 51, 53, 5... \n","2011 ({128, 1, 2, 3, 0, 71, 73, 75, 140, 17, 148, 5... \n","2005 ({0, 1, 2, 3, 132, 8, 142, 18, 152, 153, 158, ... \n","2012 ({128, 129, 130, 0, 133, 134, 7, 12, 13, 15, 2... \n","2042 ({4, 5, 9, 138, 10, 12, 13, 15, 17, 20, 21, 34... \n","2044 ({4, 5, 6, 7, 9, 10, 21, 29, 44, 45, 48, 49, 5... \n","2013 ({0, 1, 2, 3, 140, 14, 22, 23, 25, 29, 32, 33,... \n","2067 ({2, 3, 4, 5, 9, 146, 27, 38, 40, 42, 43, 49, ... \n","2062 ({4, 5, 6, 8, 12, 13, 16, 17, 20, 34, 35, 45, ... \n","2052 ({0, 1, 2, 3, 7, 136, 22, 24, 158, 31, 32, 33,... \n","2070 ({0, 1, 2, 3, 22, 24, 27, 29, 38, 39, 40, 41, ... \n","2068 ({0, 12, 13, 26, 27, 28, 29, 33, 36, 40, 42, 4... \n","2035 ({4, 5, 6, 9, 10, 12, 13, 15, 16, 17, 146, 147... \n","2030 ({0, 5, 6, 11, 13, 15, 16, 17, 146, 19, 20, 21... \n","2036 ({4, 5, 102, 91, 108, 13, 14, 12, 81, 21, 24, ... \n","2033 ({0, 1, 2, 3, 6, 18, 19, 25, 28, 33, 36, 46, 4... \n","2029 ({0, 1, 2, 3, 140, 141, 23, 24, 25, 26, 154, 2... \n","2038 ({0, 132, 133, 134, 6, 5, 9, 10, 11, 12, 13, 1... \n","2063 ({0, 1, 2, 131, 3, 140, 14, 144, 23, 25, 28, 2... \n","2061 ({0, 1, 2, 3, 4, 9, 10, 13, 144, 145, 146, 22,... \n","2059 ({4, 5, 6, 8, 12, 15, 16, 29, 35, 42, 48, 49, ... \n","2040 ({4, 5, 6, 7, 146, 147, 20, 21, 159, 34, 35, 4... \n","2056 ({0, 1, 131, 132, 134, 7, 9, 10, 11, 143, 144,... \n","2048 ({64, 0, 68, 5, 6, 9, 44, 77, 142, 80, 81, 49,... \n","2073 ({128, 129, 4, 5, 9, 10, 13, 14, 15, 17, 146, ... \n","2076 ({0, 1, 2, 3, 136, 11, 140, 141, 13, 12, 22, 3... \n","2039 ({128, 130, 5, 12, 13, 16, 17, 20, 21, 26, 35,... \n","2051 ({128, 1, 2, 0, 132, 133, 134, 135, 136, 6, 5,... \n","2049 ({4, 5, 11, 12, 13, 15, 16, 17, 26, 27, 29, 34... \n","2075 ({0, 1, 2, 131, 132, 5, 134, 6, 136, 4, 3, 144... \n","2043 ({4, 5, 6, 10, 20, 21, 48, 49, 51, 64, 65, 66,... \n","2069 ({0, 2, 131, 3, 6, 144, 18, 152, 153, 157, 31,... \n","2027 ({0, 1, 130, 3, 2, 7, 138, 140, 142, 30, 158, ... \n","2074 ({0, 1, 2, 3, 140, 18, 19, 29, 31, 32, 33, 36,... \n","2058 ({128, 1, 2, 3, 0, 6, 144, 145, 18, 36, 37, 45... \n","2055 ({0, 1, 3, 7, 8, 9, 10, 144, 153, 157, 158, 33... \n","2065 ({0, 131, 132, 134, 11, 12, 13, 19, 22, 25, 27... \n","2053 ({128, 0, 132, 5, 134, 4, 11, 110, 144, 81, 11... \n","2046 ({0, 4, 5, 13, 18, 34, 35, 44, 45, 49, 64, 65,... \n","2072 ({0, 1, 2, 3, 138, 140, 14, 17, 19, 24, 25, 31... \n","2034 ({1, 4, 7, 9, 10, 142, 143, 21, 34, 42, 68, 74... \n","2041 ({129, 130, 5, 7, 12, 13, 17, 29, 35, 40, 42, ... \n","2057 ({5, 7, 9, 10, 17, 146, 147, 20, 21, 28, 34, 4... \n","2031 ({128, 130, 4, 133, 134, 5, 12, 13, 34, 35, 43... \n","2066 ({0, 1, 2, 3, 140, 141, 152, 153, 26, 25, 28, ... \n","2064 ({0, 1, 2, 131, 132, 3, 7, 137, 144, 19, 153, ... \n","2032 ({0, 1, 2, 3, 23, 24, 25, 153, 30, 32, 33, 36,... \n","2054 ({4, 5, 6, 9, 10, 144, 145, 17, 147, 21, 159, ... \n","2071 ({4, 5, 6, 7, 9, 10, 15, 146, 21, 160, 34, 35,... \n","2060 ({0, 1, 2, 131, 132, 3, 135, 136, 9, 8, 144, 1... \n","2028 ({1, 3, 5, 7, 10, 11, 12, 13, 14, 15, 21, 28, ... \n","2045 ({128, 5, 134, 6, 12, 13, 16, 22, 34, 35, 39, ... \n","2050 ({1, 5, 6, 12, 18, 22, 38, 39, 41, 43, 44, 45,... \n","2047 ({1, 3, 4, 7, 12, 147, 148, 149, 150, 151, 20,... \n","2037 ({0, 1, 2, 3, 7, 8, 10, 48, 50, 51, 52, 56, 74... \n","2099 ({128, 0, 130, 2, 11, 13, 15, 145, 24, 29, 32,... \n","2114 ({5, 7, 9, 10, 145, 146, 147, 19, 21, 150, 151... \n","2108 ({128, 129, 4, 5, 6, 12, 13, 14, 15, 145, 17, ... \n","2104 ({1, 4, 5, 6, 12, 14, 22, 26, 33, 162, 35, 39,... \n","2078 ({0, 1, 2, 131, 3, 133, 134, 29, 34, 54, 58, 8... \n","2101 ({0, 2, 3, 140, 141, 142, 14, 17, 148, 21, 22,... \n","2110 ({128, 0, 4, 5, 10, 11, 12, 13, 16, 17, 146, 2... \n","2081 ({4, 5, 6, 9, 12, 13, 14, 15, 16, 17, 20, 158,... \n","2087 ({1, 2, 3, 10, 16, 22, 24, 25, 28, 29, 33, 39,... \n","2121 ({0, 1, 7, 136, 8, 10, 139, 141, 144, 30, 31, ... \n","2092 ({0, 1, 2, 3, 132, 4, 28, 29, 36, 45, 47, 48, ... \n","2079 ({161, 34, 6, 8, 42, 10, 76, 12, 46, 47, 112, ... \n","2080 ({5, 7, 8, 9, 10, 12, 13, 145, 146, 17, 34, 69... \n","2113 ({4, 5, 6, 9, 10, 18, 147, 20, 21, 19, 44, 45,... \n","2094 ({1, 12, 14, 16, 17, 22, 24, 27, 28, 29, 35, 3... \n","2112 ({4, 5, 7, 9, 10, 11, 12, 13, 16, 17, 27, 34, ... \n","2091 ({0, 1, 2, 131, 3, 135, 148, 152, 28, 29, 30, ... \n","2090 ({128, 1, 130, 3, 2, 0, 137, 139, 147, 152, 15... \n","2105 ({0, 129, 2, 1, 8, 140, 141, 148, 149, 22, 23,... \n","2102 ({4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... \n","2088 ({5, 12, 13, 14, 15, 16, 17, 19, 20, 21, 30, 3... \n","2109 ({7, 138, 140, 141, 13, 146, 19, 20, 21, 18, 1... \n","2084 ({7, 9, 138, 146, 19, 148, 21, 153, 154, 155, ... \n","2098 ({0, 97, 98, 1, 90, 7, 104, 105, 106, 10, 9, 8... \n","2118 ({4, 5, 6, 7, 137, 9, 144, 145, 28, 157, 158, ... \n","2119 ({0, 2, 138, 140, 14, 15, 16, 18, 22, 28, 29, ... \n","2115 ({0, 1, 2, 3, 139, 140, 22, 23, 24, 26, 30, 31... \n","2086 ({1, 4, 8, 21, 23, 151, 155, 40, 43, 45, 62, 6... \n","2124 ({0, 1, 2, 3, 22, 23, 24, 25, 31, 32, 33, 37, ... \n","2100 ({128, 131, 4, 5, 6, 10, 16, 18, 20, 21, 34, 3... \n","2117 ({128, 129, 130, 3, 133, 134, 137, 11, 21, 154... \n","2103 ({134, 7, 8, 9, 146, 27, 159, 40, 76, 77, 90, ... \n","2125 ({0, 1, 2, 3, 9, 10, 16, 21, 28, 29, 34, 36, 3... \n","2085 ({1, 130, 4, 5, 6, 9, 13, 14, 16, 17, 146, 21,... \n","2120 ({128, 129, 130, 4, 138, 12, 13, 14, 34, 35, 3... \n","2097 ({128, 129, 130, 13, 16, 17, 20, 34, 42, 44, 5... \n","2089 ({128, 5, 11, 12, 13, 14, 15, 16, 17, 22, 151,... \n","2107 ({4, 6, 10, 12, 14, 17, 20, 21, 34, 35, 44, 46... \n","2106 ({4, 5, 6, 11, 16, 17, 21, 34, 35, 44, 45, 62,... \n","2095 ({4, 5, 6, 18, 19, 20, 21, 151, 27, 156, 30, 1... \n","2093 ({0, 1, 2, 3, 139, 140, 141, 11, 148, 149, 22,... \n","2083 ({32, 1, 2, 3, 0, 37, 72, 8, 106, 75, 74, 48, ... \n","2122 ({4, 5, 15, 17, 146, 18, 20, 21, 160, 34, 35, ... \n","2111 ({128, 1, 130, 0, 133, 135, 8, 138, 139, 140, ... \n","2082 ({128, 97, 34, 35, 7, 9, 10, 11, 108, 13, 12, ... \n","2126 ({4, 6, 8, 9, 10, 13, 15, 16, 145, 146, 147, 2... \n","2116 ({7, 11, 16, 19, 21, 27, 34, 40, 46, 47, 50, 5... \n","2096 ({0, 1, 2, 131, 132, 5, 6, 141, 149, 28, 41, 5... \n","2077 ({128, 0, 4, 5, 6, 28, 34, 46, 47, 48, 49, 50,... \n","2123 ({0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 146, 23, 26, ... \n","2148 ({4, 5, 6, 13, 16, 145, 146, 147, 17, 21, 22, ... \n","2155 ({0, 1, 2, 3, 23, 25, 28, 29, 32, 33, 36, 37, ... \n","2130 ({0, 1, 2, 3, 6, 137, 11, 144, 152, 153, 27, 2... \n","2171 ({0, 129, 2, 3, 4, 1, 7, 9, 10, 14, 15, 17, 14... \n","2129 ({0, 1, 2, 3, 9, 148, 152, 27, 28, 29, 36, 38,... \n","2151 ({129, 4, 5, 6, 9, 10, 12, 13, 14, 16, 148, 21... \n","2145 ({133, 6, 5, 137, 13, 16, 17, 21, 150, 152, 34... \n","2142 ({1, 8, 9, 10, 12, 13, 14, 15, 16, 17, 147, 19... \n","2156 ({130, 4, 5, 6, 9, 11, 13, 14, 16, 17, 18, 19,... \n","2143 ({0, 3, 7, 137, 144, 145, 146, 150, 22, 30, 15... \n","2167 ({128, 4, 5, 12, 13, 14, 15, 16, 17, 20, 21, 3... \n","2144 ({128, 129, 2, 3, 1, 133, 6, 7, 8, 0, 22, 154,... \n","2147 ({0, 1, 2, 3, 6, 135, 7, 9, 18, 25, 32, 72, 73... \n","2152 ({0, 1, 3, 4, 5, 7, 9, 10, 20, 22, 32, 37, 62,... \n","2163 ({0, 1, 2, 3, 24, 25, 27, 28, 29, 32, 38, 39, ... \n","2138 ({0, 1, 2, 131, 132, 133, 134, 6, 3, 10, 17, 2... \n","2159 ({3, 4, 6, 7, 8, 14, 16, 17, 146, 18, 20, 158,... \n","2158 ({0, 1, 2, 3, 6, 8, 10, 28, 30, 161, 33, 36, 3... \n","2134 ({4, 5, 6, 8, 9, 10, 13, 14, 15, 16, 17, 34, 4... \n","2169 ({4, 5, 6, 7, 11, 12, 13, 144, 17, 16, 21, 34,... \n","2136 ({4, 5, 6, 10, 11, 14, 15, 16, 17, 146, 18, 21... \n","2137 ({4, 5, 12, 13, 146, 147, 20, 18, 150, 34, 35,... \n","2166 ({128, 129, 130, 11, 13, 14, 16, 17, 22, 33, 3... \n","2170 ({4, 5, 6, 7, 10, 26, 44, 45, 64, 65, 78, 79, ... \n","2128 ({0, 1, 2, 13, 15, 16, 17, 148, 23, 24, 25, 27... \n","2149 ({0, 1, 2, 3, 7, 8, 9, 10, 22, 23, 24, 25, 28,... \n","2172 ({0, 4, 133, 134, 7, 8, 9, 6, 5, 13, 16, 17, 2... \n","2168 ({129, 4, 5, 6, 11, 12, 13, 15, 16, 17, 21, 15... \n","2160 ({0, 1, 2, 3, 7, 8, 9, 58, 75, 77, 78, 79, 80,... \n","2154 ({0, 1, 2, 131, 3, 9, 149, 22, 26, 27, 28, 30,... \n","2161 ({0, 1, 2, 3, 145, 18, 20, 28, 29, 36, 37, 38,... \n","2140 ({128, 1, 2, 3, 4, 5, 0, 135, 8, 9, 10, 11, 7,... \n","2164 ({130, 4, 5, 12, 16, 17, 26, 27, 28, 29, 36, 4... \n","2165 ({0, 1, 2, 3, 140, 148, 23, 25, 29, 31, 32, 33... \n","2146 ({128, 1, 2, 3, 0, 134, 19, 23, 32, 33, 37, 39... \n","2150 ({0, 1, 2, 3, 9, 22, 23, 32, 33, 37, 39, 52, 5... \n","2141 ({4, 5, 6, 9, 16, 17, 20, 21, 34, 44, 48, 50, ... \n","2131 ({0, 1, 2, 3, 18, 20, 153, 37, 39, 52, 54, 55,... \n","2135 ({128, 129, 4, 5, 9, 10, 14, 17, 20, 149, 150,... \n","2127 ({0, 1, 2, 3, 4, 7, 8, 9, 138, 139, 140, 141, ... \n","2132 ({130, 7, 8, 11, 12, 14, 15, 18, 147, 151, 159... \n","2162 ({13, 17, 146, 148, 149, 150, 22, 24, 25, 27, ... \n","2157 ({160, 161, 162, 3, 1, 39, 9, 74, 75, 44, 10, ... \n","2139 ({4, 5, 6, 7, 144, 17, 16, 147, 20, 21, 151, 1... \n","2133 ({0, 129, 130, 3, 2, 1, 8, 15, 22, 23, 24, 25,... \n","2153 ({0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, ... \n","\n"," Approximation and Heuristics TSP \\\n","2019 [0, 160, 0, 86, 81, 1, 159, 1, 99, 69, 82, 85,... \n","2024 [0, 161, 4, 130, 41, 7, 92, 73, 1, 108, 56, 15... \n","2022 [0, 161, 162, 1, 79, 4, 82, 81, 150, 12, 6, 10... \n","2015 [0, 163, 0, 158, 1, 107, 61, 1, 108, 54, 1, 12... \n","2025 [0, 157, 2, 66, 101, 95, 69, 4, 82, 85, 84, 83... \n","2017 [0, 163, 0, 99, 68, 4, 76, 92, 85, 84, 91, 72,... \n","2010 [0, 120, 0, 163, 84, 85, 83, 86, 82, 0, 87, 81... \n","2020 [0, 86, 85, 87, 84, 88, 83, 93, 79, 98, 74, 97... \n","2026 [0, 158, 3, 64, 115, 1, 160, 104, 63, 2, 137, ... \n","2023 [0, 163, 162, 1, 145, 24, 7, 140, 31, 57, 121,... \n","2001 [0, 161, 158, 3, 69, 104, 87, 84, 88, 83, 91, ... \n","2018 [0, 126, 42, 2, 61, 108, 85, 84, 87, 83, 0, 88... \n","2007 [0, 163, 156, 2, 68, 93, 96, 75, 1, 88, 86, 85... \n","2002 [0, 160, 0, 99, 68, 1, 163, 94, 73, 74, 97, 4,... \n","2009 [0, 85, 83, 87, 80, 93, 79, 88, 77, 89, 76, 90... \n","2016 [0, 88, 87, 84, 83, 85, 82, 86, 81, 92, 80, 0,... \n","2006 [0, 161, 157, 3, 111, 63, 1, 64, 103, 4, 114, ... \n","2003 [0, 128, 43, 4, 114, 58, 46, 126, 85, 84, 86, ... \n","2008 [0, 162, 1, 70, 100, 96, 69, 1, 101, 62, 78, 9... \n","2014 [0, 158, 122, 42, 2, 159, 1, 163, 97, 69, 107,... \n","2021 [0, 163, 162, 4, 129, 34, 6, 91, 67, 1, 100, 7... \n","2004 [0, 158, 85, 83, 0, 84, 159, 4, 81, 87, 80, 0,... \n","2011 [0, 162, 1, 94, 77, 96, 72, 103, 70, 1, 102, 6... \n","2005 [0, 162, 158, 2, 108, 70, 4, 71, 97, 1, 163, 1... \n","2012 [0, 162, 0, 84, 83, 87, 81, 88, 80, 86, 79, 98... \n","2042 [0, 160, 0, 132, 44, 4, 138, 28, 5, 57, 111, 1... \n","2044 [0, 153, 141, 20, 3, 138, 31, 150, 21, 67, 101... \n","2013 [0, 161, 162, 3, 49, 128, 0, 85, 84, 87, 83, 8... \n","2067 [0, 162, 1, 105, 62, 2, 69, 98, 88, 77, 101, 6... \n","2062 [0, 161, 85, 0, 87, 84, 0, 162, 1, 88, 83, 93,... \n","2052 [0, 131, 44, 4, 117, 57, 1, 62, 116, 106, 76, ... \n","2070 [0, 84, 83, 85, 82, 0, 87, 80, 92, 73, 0, 96, ... \n","2068 [0, 163, 0, 101, 61, 11, 17, 149, 1, 150, 16, ... \n","2035 [0, 163, 2, 68, 103, 1, 105, 69, 1, 100, 67, 2... \n","2030 [0, 84, 81, 85, 80, 88, 77, 92, 73, 94, 72, 93... \n","2036 [0, 142, 0, 115, 49, 2, 69, 95, 111, 57, 5, 16... \n","2033 [0, 85, 84, 86, 83, 89, 82, 90, 81, 0, 87, 80,... \n","2029 [0, 161, 2, 78, 95, 85, 82, 4, 81, 84, 87, 83,... \n","2038 [0, 163, 99, 69, 4, 160, 4, 81, 84, 83, 82, 85... \n","2063 [0, 160, 2, 65, 104, 1, 98, 69, 74, 97, 0, 99,... \n","2061 [0, 163, 3, 45, 120, 1, 161, 1, 90, 73, 109, 6... \n","2059 [0, 99, 72, 1, 160, 1, 73, 96, 0, 158, 10, 6, ... \n","2040 [0, 91, 79, 7, 162, 40, 127, 2, 155, 109, 64, ... \n","2056 [0, 162, 127, 45, 1, 108, 63, 114, 57, 50, 119... \n","2048 [0, 84, 83, 85, 82, 86, 81, 0, 88, 80, 87, 79,... \n","2073 [0, 156, 148, 83, 85, 80, 88, 75, 87, 73, 91, ... \n","2076 [0, 162, 1, 155, 3, 104, 68, 110, 61, 111, 56,... \n","2039 [0, 163, 144, 26, 5, 148, 4, 91, 69, 98, 68, 7... \n","2051 [0, 162, 0, 157, 1, 100, 69, 4, 139, 28, 61, 1... \n","2049 [0, 123, 46, 4, 81, 86, 1, 156, 100, 67, 107, ... \n","2075 [0, 162, 96, 77, 4, 70, 94, 99, 69, 76, 93, 10... \n","2043 [0, 162, 97, 76, 4, 100, 67, 77, 95, 96, 75, 1... \n","2069 [0, 123, 42, 1, 91, 68, 63, 104, 0, 124, 41, 6... \n","2027 [0, 162, 119, 48, 1, 96, 74, 108, 63, 105, 62,... \n","2074 [0, 92, 71, 1, 151, 78, 89, 84, 83, 97, 69, 82... \n","2058 [0, 163, 0, 129, 44, 3, 90, 76, 109, 66, 68, 1... \n","2055 [0, 163, 162, 3, 142, 31, 32, 130, 4, 159, 160... \n","2065 [0, 162, 93, 69, 4, 81, 86, 85, 83, 87, 80, 95... \n","2053 [0, 163, 97, 74, 1, 75, 96, 98, 69, 1, 76, 95,... \n","2046 [0, 162, 2, 78, 88, 87, 83, 85, 82, 0, 91, 80,... \n","2072 [0, 163, 85, 86, 84, 87, 83, 88, 80, 93, 79, 9... \n","2034 [0, 159, 2, 72, 96, 0, 122, 46, 48, 119, 1, 79... \n","2041 [0, 161, 159, 2, 66, 98, 160, 1, 151, 4, 70, 9... \n","2057 [0, 158, 84, 83, 85, 82, 87, 80, 96, 73, 88, 7... \n","2031 [0, 163, 0, 103, 66, 4, 99, 68, 69, 98, 104, 6... \n","2066 [0, 162, 85, 84, 88, 83, 92, 80, 93, 76, 94, 7... \n","2064 [0, 153, 20, 3, 68, 67, 100, 4, 127, 139, 1, 1... \n","2032 [0, 162, 102, 69, 1, 70, 101, 100, 68, 98, 67,... \n","2054 [0, 162, 7, 16, 157, 95, 75, 1, 79, 89, 161, 3... \n","2071 [0, 162, 1, 86, 81, 94, 71, 99, 68, 107, 63, 6... \n","2060 [0, 162, 1, 154, 4, 105, 72, 2, 161, 0, 126, 4... \n","2028 [0, 104, 63, 1, 88, 79, 89, 78, 98, 69, 109, 6... \n","2045 [0, 162, 1, 161, 4, 109, 58, 5, 70, 94, 1, 92,... \n","2050 [0, 85, 81, 1, 163, 84, 0, 87, 82, 0, 88, 80, ... \n","2047 [0, 123, 45, 4, 18, 147, 1, 86, 81, 88, 79, 89... \n","2037 [0, 163, 121, 42, 2, 162, 2, 70, 91, 84, 83, 8... \n","2099 [0, 162, 2, 61, 106, 101, 74, 1, 88, 82, 99, 7... \n","2114 [0, 100, 74, 1, 69, 107, 4, 108, 68, 77, 96, 1... \n","2108 [0, 160, 0, 100, 69, 2, 70, 91, 85, 84, 92, 83... \n","2104 [0, 161, 0, 123, 40, 4, 162, 1, 163, 90, 75, 9... \n","2078 [0, 161, 96, 74, 1, 160, 1, 98, 69, 70, 95, 99... \n","2101 [0, 163, 87, 84, 85, 80, 83, 79, 0, 88, 78, 0,... \n","2110 [0, 160, 84, 83, 86, 81, 87, 80, 90, 76, 0, 91... \n","2081 [0, 130, 41, 1, 163, 1, 93, 71, 98, 70, 99, 68... \n","2087 [0, 127, 69, 1, 157, 1, 88, 73, 99, 71, 101, 6... \n","2121 [0, 133, 34, 4, 108, 64, 111, 57, 118, 48, 115... \n","2092 [0, 96, 70, 1, 161, 1, 81, 86, 103, 69, 82, 85... \n","2079 [0, 158, 0, 85, 84, 87, 80, 0, 92, 75, 96, 72,... \n","2080 [0, 160, 159, 6, 50, 119, 0, 157, 84, 85, 83, ... \n","2113 [0, 163, 152, 14, 11, 118, 46, 4, 92, 70, 109,... \n","2094 [0, 84, 83, 85, 82, 86, 81, 87, 80, 0, 95, 77,... \n","2112 [0, 148, 19, 5, 66, 102, 0, 154, 18, 21, 142, ... \n","2091 [0, 99, 71, 5, 77, 91, 85, 84, 0, 94, 83, 88, ... \n","2090 [0, 162, 159, 3, 105, 63, 1, 99, 61, 57, 109, ... \n","2105 [0, 162, 147, 19, 2, 79, 1, 46, 122, 99, 68, 3... \n","2102 [0, 163, 0, 85, 84, 87, 83, 86, 81, 88, 80, 93... \n","2088 [0, 161, 1, 100, 69, 58, 119, 123, 68, 5, 71, ... \n","2109 [0, 151, 17, 7, 140, 31, 5, 159, 1, 101, 68, 1... \n","2084 [0, 116, 49, 2, 99, 68, 3, 163, 67, 103, 0, 88... \n","2098 [0, 109, 55, 2, 160, 2, 107, 57, 114, 49, 72, ... \n","2118 [0, 142, 87, 84, 0, 163, 83, 93, 80, 90, 76, 9... \n","2119 [0, 84, 83, 85, 80, 96, 75, 87, 73, 93, 72, 0,... \n","2115 [0, 161, 2, 66, 110, 4, 163, 6, 120, 48, 122, ... \n","2086 [0, 86, 85, 87, 84, 0, 88, 83, 0, 89, 82, 90, ... \n","2124 [0, 158, 3, 42, 125, 0, 131, 40, 3, 62, 108, 4... \n","2100 [0, 163, 84, 85, 83, 87, 80, 94, 78, 79, 89, 3... \n","2117 [0, 141, 159, 4, 45, 127, 3, 128, 44, 67, 102,... \n","2103 [0, 162, 0, 125, 42, 8, 56, 114, 87, 84, 86, 8... \n","2125 [0, 125, 42, 2, 43, 124, 126, 41, 108, 64, 4, ... \n","2085 [0, 162, 0, 117, 51, 1, 160, 89, 78, 90, 77, 1... \n","2120 [0, 163, 0, 162, 5, 31, 144, 104, 62, 1, 61, 1... \n","2097 [0, 163, 161, 1, 62, 107, 8, 32, 135, 0, 160, ... \n","2089 [0, 163, 162, 2, 72, 99, 4, 108, 60, 7, 122, 5... \n","2107 [0, 158, 0, 94, 69, 3, 89, 78, 90, 77, 98, 71,... \n","2106 [0, 100, 68, 3, 79, 95, 162, 2, 70, 91, 0, 163... \n","2095 [0, 152, 0, 93, 81, 4, 69, 86, 92, 67, 4, 157,... \n","2093 [0, 163, 162, 2, 78, 90, 4, 89, 79, 94, 77, 11... \n","2083 [0, 133, 157, 1, 163, 84, 85, 83, 93, 80, 94, ... \n","2122 [0, 163, 85, 83, 87, 80, 88, 79, 89, 78, 0, 94... \n","2111 [0, 116, 109, 68, 2, 66, 104, 163, 1, 76, 98, ... \n","2082 [0, 163, 158, 1, 127, 43, 7, 91, 78, 30, 144, ... \n","2126 [0, 161, 0, 87, 84, 88, 83, 92, 63, 2, 162, 91... \n","2116 [0, 161, 5, 47, 120, 3, 160, 0, 85, 84, 86, 83... \n","2096 [0, 162, 1, 133, 35, 71, 93, 140, 24, 1, 82, 8... \n","2077 [0, 154, 20, 8, 163, 63, 105, 0, 126, 42, 2, 1... \n","2123 [0, 163, 2, 82, 88, 1, 24, 135, 154, 21, 45, 1... \n","2148 [0, 93, 71, 4, 97, 70, 78, 91, 102, 67, 3, 79,... \n","2155 [0, 127, 40, 2, 42, 123, 161, 3, 67, 107, 4, 9... \n","2130 [0, 121, 49, 4, 109, 65, 67, 102, 117, 42, 107... \n","2171 [0, 85, 84, 86, 83, 0, 87, 82, 88, 81, 89, 80,... \n","2129 [0, 162, 1, 81, 83, 84, 82, 85, 80, 87, 77, 76... \n","2151 [0, 159, 118, 45, 3, 50, 117, 120, 48, 4, 65, ... \n","2145 [0, 156, 158, 1, 154, 3, 63, 107, 116, 51, 34,... \n","2142 [0, 163, 100, 63, 1, 76, 90, 3, 98, 70, 105, 6... \n","2156 [0, 162, 138, 29, 3, 57, 112, 4, 71, 104, 85, ... \n","2143 [0, 162, 3, 112, 57, 1, 109, 53, 1, 110, 52, 5... \n","2167 [0, 163, 0, 119, 62, 1, 105, 58, 1, 57, 104, 9... \n","2144 [0, 162, 1, 97, 71, 109, 64, 67, 102, 160, 3, ... \n","2147 [0, 162, 129, 41, 2, 66, 107, 4, 109, 65, 67, ... \n","2152 [0, 116, 49, 4, 51, 115, 161, 3, 64, 103, 0, 9... \n","2163 [0, 132, 0, 162, 85, 87, 84, 88, 83, 97, 75, 1... \n","2138 [0, 158, 3, 39, 124, 0, 161, 84, 85, 83, 93, 8... \n","2159 [0, 162, 0, 95, 74, 2, 89, 78, 3, 97, 70, 90, ... \n","2158 [0, 84, 83, 85, 82, 0, 93, 80, 87, 79, 88, 78,... \n","2134 [0, 158, 1, 93, 74, 70, 97, 0, 99, 69, 104, 65... \n","2169 [0, 162, 160, 2, 70, 95, 1, 130, 1, 90, 74, 97... \n","2136 [0, 163, 162, 3, 64, 109, 119, 46, 2, 70, 92, ... \n","2137 [0, 162, 1, 67, 99, 102, 66, 63, 110, 4, 111, ... \n","2166 [0, 162, 3, 50, 118, 4, 159, 103, 67, 1, 163, ... \n","2170 [0, 154, 17, 3, 70, 107, 4, 163, 89, 82, 90, 8... \n","2128 [0, 85, 83, 86, 80, 0, 95, 79, 88, 75, 91, 73,... \n","2149 [0, 162, 1, 57, 110, 4, 82, 111, 56, 118, 44, ... \n","2172 [0, 161, 114, 58, 10, 15, 152, 1, 155, 14, 3, ... \n","2168 [0, 163, 156, 2, 70, 95, 162, 1, 99, 67, 71, 9... \n","2160 [0, 103, 68, 1, 67, 101, 108, 63, 74, 97, 109,... \n","2154 [0, 96, 69, 2, 70, 93, 101, 66, 68, 107, 5, 13... \n","2161 [0, 86, 84, 85, 83, 87, 80, 88, 77, 0, 94, 81,... \n","2140 [0, 161, 0, 84, 83, 85, 82, 86, 81, 87, 80, 88... \n","2164 [0, 162, 141, 27, 4, 68, 107, 1, 163, 2, 29, 1... \n","2165 [0, 163, 162, 2, 94, 68, 3, 160, 1, 63, 105, 4... \n","2146 [0, 157, 1, 95, 71, 100, 67, 59, 109, 4, 163, ... \n","2150 [0, 160, 0, 119, 45, 4, 163, 82, 81, 93, 70, 6... \n","2141 [0, 156, 0, 125, 46, 1, 163, 64, 110, 3, 88, 8... \n","2131 [0, 162, 2, 62, 106, 91, 79, 7, 122, 56, 4, 82... \n","2135 [0, 93, 72, 1, 91, 73, 1, 161, 4, 82, 86, 0, 9... \n","2127 [0, 84, 83, 85, 82, 86, 80, 87, 79, 89, 77, 88... \n","2132 [0, 85, 84, 86, 83, 87, 82, 90, 78, 3, 89, 81,... \n","2162 [0, 145, 40, 1, 71, 98, 3, 99, 69, 63, 108, 4,... \n","2157 [0, 159, 98, 73, 1, 162, 1, 87, 81, 3, 163, 2,... \n","2139 [0, 162, 92, 70, 4, 86, 81, 77, 90, 3, 159, 89... \n","2133 [0, 163, 104, 66, 4, 156, 86, 81, 99, 68, 67, ... \n","2153 [0, 153, 101, 67, 1, 71, 100, 0, 145, 29, 2, 7... \n","\n"," Approximation and Heuristics treewidth Min Degree \\\n","2019 127.0 \n","2024 144.0 \n","2022 140.0 \n","2015 131.0 \n","2025 142.0 \n","2017 146.0 \n","2010 137.0 \n","2020 144.0 \n","2026 138.0 \n","2023 146.0 \n","2001 129.0 \n","2018 140.0 \n","2007 144.0 \n","2002 139.0 \n","2009 139.0 \n","2016 137.0 \n","2006 148.0 \n","2003 144.0 \n","2008 142.0 \n","2014 136.0 \n","2021 135.0 \n","2004 147.0 \n","2011 140.0 \n","2005 146.0 \n","2012 137.0 \n","2042 145.0 \n","2044 137.0 \n","2013 129.0 \n","2067 141.0 \n","2062 144.0 \n","2052 142.0 \n","2070 140.0 \n","2068 130.0 \n","2035 138.0 \n","2030 137.0 \n","2036 146.0 \n","2033 140.0 \n","2029 143.0 \n","2038 136.0 \n","2063 141.0 \n","2061 139.0 \n","2059 135.0 \n","2040 135.0 \n","2056 145.0 \n","2048 142.0 \n","2073 132.0 \n","2076 144.0 \n","2039 148.0 \n","2051 142.0 \n","2049 146.0 \n","2075 143.0 \n","2043 142.0 \n","2069 136.0 \n","2027 143.0 \n","2074 139.0 \n","2058 143.0 \n","2055 125.0 \n","2065 135.0 \n","2053 140.0 \n","2046 126.0 \n","2072 151.0 \n","2034 144.0 \n","2041 142.0 \n","2057 139.0 \n","2031 137.0 \n","2066 140.0 \n","2064 141.0 \n","2032 143.0 \n","2054 134.0 \n","2071 124.0 \n","2060 143.0 \n","2028 143.0 \n","2045 136.0 \n","2050 146.0 \n","2047 147.0 \n","2037 142.0 \n","2099 149.0 \n","2114 130.0 \n","2108 134.0 \n","2104 144.0 \n","2078 142.0 \n","2101 140.0 \n","2110 142.0 \n","2081 146.0 \n","2087 144.0 \n","2121 142.0 \n","2092 140.0 \n","2079 141.0 \n","2080 143.0 \n","2113 147.0 \n","2094 140.0 \n","2112 131.0 \n","2091 141.0 \n","2090 144.0 \n","2105 127.0 \n","2102 143.0 \n","2088 138.0 \n","2109 145.0 \n","2084 141.0 \n","2098 132.0 \n","2118 119.0 \n","2119 144.0 \n","2115 137.0 \n","2086 141.0 \n","2124 143.0 \n","2100 146.0 \n","2117 142.0 \n","2103 143.0 \n","2125 142.0 \n","2085 144.0 \n","2120 127.0 \n","2097 137.0 \n","2089 144.0 \n","2107 145.0 \n","2106 127.0 \n","2095 145.0 \n","2093 143.0 \n","2083 145.0 \n","2122 136.0 \n","2111 145.0 \n","2082 130.0 \n","2126 145.0 \n","2116 146.0 \n","2096 142.0 \n","2077 147.0 \n","2123 142.0 \n","2148 146.0 \n","2155 145.0 \n","2130 145.0 \n","2171 137.0 \n","2129 146.0 \n","2151 146.0 \n","2145 143.0 \n","2142 127.0 \n","2156 135.0 \n","2143 143.0 \n","2167 140.0 \n","2144 140.0 \n","2147 144.0 \n","2152 134.0 \n","2163 141.0 \n","2138 136.0 \n","2159 143.0 \n","2158 131.0 \n","2134 145.0 \n","2169 144.0 \n","2136 140.0 \n","2137 138.0 \n","2166 136.0 \n","2170 132.0 \n","2128 129.0 \n","2149 129.0 \n","2172 140.0 \n","2168 147.0 \n","2160 144.0 \n","2154 136.0 \n","2161 131.0 \n","2140 139.0 \n","2164 148.0 \n","2165 147.0 \n","2146 144.0 \n","2150 138.0 \n","2141 143.0 \n","2131 138.0 \n","2135 142.0 \n","2127 133.0 \n","2132 146.0 \n","2162 142.0 \n","2157 144.0 \n","2139 142.0 \n","2133 144.0 \n","2153 143.0 \n","\n"," Approximation and Heuristics treewidth Min Fill In \\\n","2019 127.0 \n","2024 144.0 \n","2022 140.0 \n","2015 131.0 \n","2025 142.0 \n","2017 146.0 \n","2010 137.0 \n","2020 144.0 \n","2026 138.0 \n","2023 146.0 \n","2001 129.0 \n","2018 140.0 \n","2007 144.0 \n","2002 139.0 \n","2009 139.0 \n","2016 137.0 \n","2006 148.0 \n","2003 144.0 \n","2008 142.0 \n","2014 136.0 \n","2021 135.0 \n","2004 147.0 \n","2011 140.0 \n","2005 146.0 \n","2012 137.0 \n","2042 145.0 \n","2044 137.0 \n","2013 129.0 \n","2067 141.0 \n","2062 144.0 \n","2052 142.0 \n","2070 140.0 \n","2068 130.0 \n","2035 138.0 \n","2030 137.0 \n","2036 146.0 \n","2033 140.0 \n","2029 143.0 \n","2038 136.0 \n","2063 141.0 \n","2061 139.0 \n","2059 135.0 \n","2040 135.0 \n","2056 145.0 \n","2048 142.0 \n","2073 132.0 \n","2076 144.0 \n","2039 148.0 \n","2051 142.0 \n","2049 146.0 \n","2075 143.0 \n","2043 142.0 \n","2069 136.0 \n","2027 143.0 \n","2074 139.0 \n","2058 143.0 \n","2055 125.0 \n","2065 135.0 \n","2053 140.0 \n","2046 126.0 \n","2072 151.0 \n","2034 144.0 \n","2041 142.0 \n","2057 139.0 \n","2031 137.0 \n","2066 140.0 \n","2064 141.0 \n","2032 143.0 \n","2054 134.0 \n","2071 124.0 \n","2060 143.0 \n","2028 143.0 \n","2045 136.0 \n","2050 146.0 \n","2047 147.0 \n","2037 142.0 \n","2099 149.0 \n","2114 130.0 \n","2108 134.0 \n","2104 144.0 \n","2078 142.0 \n","2101 140.0 \n","2110 142.0 \n","2081 146.0 \n","2087 144.0 \n","2121 142.0 \n","2092 140.0 \n","2079 141.0 \n","2080 143.0 \n","2113 147.0 \n","2094 140.0 \n","2112 131.0 \n","2091 141.0 \n","2090 144.0 \n","2105 127.0 \n","2102 143.0 \n","2088 138.0 \n","2109 145.0 \n","2084 141.0 \n","2098 132.0 \n","2118 119.0 \n","2119 144.0 \n","2115 137.0 \n","2086 141.0 \n","2124 143.0 \n","2100 146.0 \n","2117 142.0 \n","2103 143.0 \n","2125 142.0 \n","2085 144.0 \n","2120 127.0 \n","2097 137.0 \n","2089 144.0 \n","2107 145.0 \n","2106 127.0 \n","2095 145.0 \n","2093 143.0 \n","2083 145.0 \n","2122 136.0 \n","2111 145.0 \n","2082 130.0 \n","2126 145.0 \n","2116 146.0 \n","2096 142.0 \n","2077 147.0 \n","2123 142.0 \n","2148 146.0 \n","2155 145.0 \n","2130 145.0 \n","2171 137.0 \n","2129 146.0 \n","2151 146.0 \n","2145 143.0 \n","2142 127.0 \n","2156 135.0 \n","2143 143.0 \n","2167 140.0 \n","2144 140.0 \n","2147 144.0 \n","2152 134.0 \n","2163 141.0 \n","2138 136.0 \n","2159 143.0 \n","2158 131.0 \n","2134 145.0 \n","2169 144.0 \n","2136 140.0 \n","2137 138.0 \n","2166 136.0 \n","2170 132.0 \n","2128 129.0 \n","2149 129.0 \n","2172 140.0 \n","2168 147.0 \n","2160 144.0 \n","2154 136.0 \n","2161 131.0 \n","2140 139.0 \n","2164 148.0 \n","2165 147.0 \n","2146 144.0 \n","2150 138.0 \n","2141 143.0 \n","2131 138.0 \n","2135 142.0 \n","2127 133.0 \n","2132 146.0 \n","2162 142.0 \n","2157 144.0 \n","2139 142.0 \n","2133 144.0 \n","2153 143.0 \n","\n"," Approximation and Heuristics treewidth Min Wt Vertex Cover \\\n","2019 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2024 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2022 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2015 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2025 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2017 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2010 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2020 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2026 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2023 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2001 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2018 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2007 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2002 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2009 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2016 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2006 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2003 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2008 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2014 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2021 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2004 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2011 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2005 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2012 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2042 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2044 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2013 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2067 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2062 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2052 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2070 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2068 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2035 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2030 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2036 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2033 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2029 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2038 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2063 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2061 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2059 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2040 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2056 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2048 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2073 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2076 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2039 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2051 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2049 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2075 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2043 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2069 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2027 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2074 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2058 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2055 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2065 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2053 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2046 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2072 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2034 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2041 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2057 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2031 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2066 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2064 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2032 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2054 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2071 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2060 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2028 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2045 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2050 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2047 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2037 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2099 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2114 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2108 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2104 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2078 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2101 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2110 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2081 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2087 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2121 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2092 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2079 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2080 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2113 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2094 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2112 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2091 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2090 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2105 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2102 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2088 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2109 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2084 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2098 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2118 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2119 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2115 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2086 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2124 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2100 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2117 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2103 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2125 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2085 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2120 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2097 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2089 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2107 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2106 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2095 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2093 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2083 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2122 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2111 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2082 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2126 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2116 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2096 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2077 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2123 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2148 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2155 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2130 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2171 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2129 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2151 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2145 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2142 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2156 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2143 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2167 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2144 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2147 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2152 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2163 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2138 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2159 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2158 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2134 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2169 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2136 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2137 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2166 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2170 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2128 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2149 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2172 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2168 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2160 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2154 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2161 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2140 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2164 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2165 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2146 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2150 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2141 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2131 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2135 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2127 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2132 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2162 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2157 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2139 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2133 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","2153 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... \n","\n"," Approximation and Heuristics Randomized Partitioning \\\n","2019 (3769, ({0, 1, 2, 3, 4, 5, 7, 9, 12, 14, 17, 1... \n","2024 (3699, ({2, 3, 6, 7, 9, 14, 20, 21, 22, 23, 24... \n","2022 (3750, ({8, 10, 12, 13, 14, 16, 19, 22, 25, 26... \n","2015 (3400, ({0, 1, 2, 3, 4, 6, 10, 12, 14, 16, 17,... \n","2025 (3768, ({1, 2, 4, 5, 6, 8, 10, 11, 14, 15, 16,... \n","2017 (3902, ({1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 14, ... \n","2010 (3664, ({0, 1, 3, 5, 6, 8, 9, 10, 12, 14, 17, ... \n","2020 (3646, ({1, 3, 4, 7, 9, 10, 11, 12, 15, 16, 18... \n","2026 (3564, ({1, 2, 3, 5, 7, 9, 12, 13, 18, 21, 23,... \n","2023 (3582, ({0, 1, 5, 7, 8, 10, 11, 16, 17, 18, 20... \n","2001 (3443, ({1, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20,... \n","2018 (3586, ({0, 1, 2, 4, 9, 10, 12, 13, 14, 16, 18... \n","2007 (3645, ({2, 4, 5, 6, 7, 8, 10, 11, 13, 21, 22,... \n","2002 (3926, ({0, 1, 2, 5, 6, 8, 10, 12, 13, 14, 15,... \n","2009 (3810, ({0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12... \n","2016 (3581, ({128, 2, 3, 4, 131, 134, 8, 9, 10, 11,... \n","2006 (4208, ({1, 4, 5, 7, 8, 10, 11, 13, 14, 15, 19... \n","2003 (3884, ({1, 3, 6, 7, 9, 10, 11, 12, 16, 17, 19... \n","2008 (3947, ({0, 1, 3, 131, 134, 135, 8, 9, 137, 11... \n","2014 (3721, ({0, 128, 130, 4, 133, 134, 7, 8, 135, ... \n","2021 (3423, ({0, 1, 5, 8, 9, 10, 14, 15, 16, 17, 18... \n","2004 (3729, ({0, 1, 3, 4, 9, 12, 13, 15, 16, 18, 23... \n","2011 (3814, ({0, 4, 5, 6, 8, 11, 15, 19, 20, 21, 22... \n","2005 (3679, ({0, 128, 130, 3, 4, 132, 133, 8, 9, 10... \n","2012 (4906, ({1, 2, 4, 5, 10, 13, 14, 15, 16, 23, 2... \n","2042 (3651, ({0, 1, 5, 6, 7, 8, 12, 13, 17, 20, 21,... \n","2044 (3504, ({4, 6, 7, 10, 11, 12, 13, 14, 16, 17, ... \n","2013 (3484, ({1, 3, 5, 6, 9, 11, 13, 14, 16, 20, 21... \n","2067 (3435, ({0, 1, 2, 8, 11, 12, 13, 17, 18, 19, 2... \n","2062 (3515, ({0, 1, 2, 4, 5, 7, 10, 12, 15, 16, 18,... \n","2052 (3584, ({0, 1, 3, 5, 6, 8, 12, 16, 20, 22, 24,... \n","2070 (3429, ({0, 2, 3, 5, 8, 11, 13, 16, 18, 20, 21... \n","2068 (3811, ({0, 2, 3, 5, 14, 15, 20, 21, 26, 28, 2... \n","2035 (3648, ({0, 1, 4, 7, 9, 13, 15, 16, 18, 19, 22... \n","2030 (4453, ({0, 3, 4, 6, 7, 8, 9, 10, 13, 15, 16, ... \n","2036 (3789, ({3, 5, 6, 7, 10, 12, 14, 18, 21, 23, 2... \n","2033 (4256, ({0, 2, 3, 4, 5, 6, 11, 15, 18, 24, 26,... \n","2029 (3427, ({1, 5, 6, 12, 13, 17, 19, 20, 22, 23, ... \n","2038 (4533, ({0, 1, 5, 6, 7, 9, 11, 13, 21, 23, 24,... \n","2063 (3787, ({3, 6, 7, 8, 9, 10, 14, 17, 21, 23, 24... \n","2061 (3749, ({0, 1, 2, 4, 6, 7, 10, 11, 13, 15, 16,... \n","2059 (3426, ({5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 1... \n","2040 (3507, ({0, 2, 4, 5, 6, 7, 8, 9, 10, 12, 20, 2... \n","2056 (3639, ({129, 132, 5, 6, 133, 8, 135, 10, 136,... \n","2048 (3622, ({0, 1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 1... \n","2073 (3440, ({0, 1, 5, 8, 10, 11, 13, 17, 18, 19, 2... \n","2076 (3885, ({0, 1, 2, 3, 5, 6, 10, 11, 16, 18, 20,... \n","2039 (3892, ({0, 2, 4, 5, 6, 7, 9, 10, 12, 20, 26, ... \n","2051 (3662, ({0, 2, 3, 6, 8, 13, 15, 16, 17, 21, 22... \n","2049 (3507, ({128, 2, 131, 132, 7, 8, 135, 137, 11,... \n","2075 (4320, ({0, 2, 3, 4, 6, 8, 9, 12, 14, 15, 16, ... \n","2043 (3598, ({0, 1, 2, 129, 4, 5, 131, 7, 134, 140,... \n","2069 (3689, ({0, 1, 6, 8, 16, 17, 25, 28, 31, 34, 3... \n","2027 (3830, ({2, 3, 5, 8, 10, 13, 14, 18, 20, 21, 2... \n","2074 (3454, ({0, 2, 6, 8, 10, 12, 13, 14, 16, 17, 1... \n","2058 (3964, ({2, 6, 11, 15, 16, 17, 18, 19, 20, 22,... \n","2055 (3699, ({0, 1, 2, 3, 6, 8, 10, 11, 12, 16, 17,... \n","2065 (3699, ({0, 1, 4, 6, 7, 9, 10, 11, 17, 18, 20,... \n","2053 (3697, ({0, 1, 2, 3, 7, 8, 9, 11, 12, 13, 14, ... \n","2046 (3863, ({130, 4, 132, 134, 7, 8, 9, 135, 137, ... \n","2072 (4022, ({1, 2, 4, 6, 16, 23, 25, 28, 29, 34, 3... \n","2034 (4380, ({3, 4, 8, 12, 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({3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17,... \n","2141 (3354, ({2, 3, 4, 6, 8, 9, 15, 16, 18, 19, 21,... \n","2131 (3694, ({0, 130, 3, 4, 5, 6, 7, 131, 9, 132, 1... \n","2135 (3958, ({1, 2, 3, 5, 6, 7, 9, 10, 11, 14, 16, ... \n","2127 (3935, ({128, 1, 2, 6, 134, 8, 139, 13, 141, 1... \n","2132 (4266, ({4, 5, 7, 8, 9, 10, 12, 16, 17, 19, 21... \n","2162 (3665, ({0, 1, 3, 4, 8, 12, 14, 15, 18, 20, 22... \n","2157 (3719, ({0, 1, 3, 5, 6, 12, 15, 17, 18, 19, 21... \n","2139 (3957, ({2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15,... \n","2133 (3818, ({1, 2, 3, 7, 8, 9, 12, 13, 14, 17, 19,... \n","2153 (4084, ({0, 129, 3, 4, 131, 133, 7, 134, 9, 10... \n","\n"," Approximation and Heuristics One Exchange Degree Assortativity \\\n","2019 (4076, ({0, 1, 2, 6, 11, 14, 15, 16, 17, 20, 2... 0.320875 \n","2024 (4000, ({1, 2, 3, 5, 6, 11, 12, 13, 14, 15, 16... 0.173836 \n","2022 (4069, ({0, 3, 4, 8, 10, 13, 14, 15, 17, 18, 1... 0.158501 \n","2015 (3712, ({0, 1, 4, 5, 6, 11, 12, 13, 14, 15, 19... 0.091587 \n","2025 (4032, ({1, 4, 8, 9, 10, 12, 13, 14, 18, 21, 2... 0.094496 \n","2017 (4188, ({2, 3, 4, 6, 12, 13, 14, 16, 22, 24, 2... 0.142865 \n","2010 (4001, ({0, 1, 2, 4, 5, 6, 8, 9, 10, 11, 12, 1... 0.218099 \n","2020 (3962, ({18, 21, 22, 24, 26, 27, 28, 29, 30, 3... 0.156659 \n","2026 (3799, ({0, 2, 5, 6, 9, 10, 12, 13, 14, 15, 18... 0.073258 \n","2023 (3886, ({0, 1, 2, 3, 5, 6, 11, 12, 13, 14, 17,... 0.128423 \n","2001 (3721, ({0, 6, 11, 13, 15, 18, 20, 22, 23, 26,... 0.077016 \n","2018 (3821, ({1, 9, 14, 15, 17, 18, 19, 21, 22, 24,... 0.234087 \n","2007 (3952, ({0, 1, 2, 8, 9, 15, 16, 18, 20, 21, 23... 0.146979 \n","2002 (4266, ({2, 3, 4, 5, 6, 7, 10, 14, 15, 17, 18,... 0.136600 \n","2009 (4082, ({1, 2, 4, 5, 9, 10, 19, 22, 27, 28, 29... 0.202940 \n","2016 (3889, ({2, 5, 6, 7, 8, 10, 14, 17, 18, 19, 20... 0.092618 \n","2006 (4420, ({2, 3, 4, 5, 10, 11, 18, 20, 21, 22, 2... 0.072866 \n","2003 (4124, ({0, 1, 9, 10, 13, 16, 22, 27, 29, 30, ... 0.107629 \n","2008 (4286, ({0, 3, 16, 17, 18, 19, 20, 21, 26, 27,... 0.143386 \n","2014 (4006, ({2, 5, 7, 8, 11, 15, 16, 17, 18, 19, 2... 0.115936 \n","2021 (3692, ({0, 2, 4, 5, 6, 9, 10, 11, 12, 13, 14,... 0.061771 \n","2004 (3943, ({0, 1, 4, 5, 7, 8, 16, 18, 21, 22, 26,... 0.148396 \n","2011 (4106, ({0, 1, 4, 5, 6, 9, 10, 12, 14, 15, 17,... 0.111769 \n","2005 (4006, ({6, 8, 13, 15, 16, 17, 22, 23, 24, 25,... 0.149463 \n","2012 (5170, ({1, 2, 5, 6, 8, 9, 12, 13, 20, 21, 22,... 0.170094 \n","2042 (3940, ({7, 8, 11, 14, 16, 20, 21, 22, 23, 28,... 0.158284 \n","2044 (3802, ({2, 6, 8, 12, 13, 15, 16, 17, 18, 19, ... 0.215561 \n","2013 (3801, ({0, 3, 9, 10, 14, 19, 20, 22, 26, 29, ... 0.125164 \n","2067 (3775, ({3, 8, 9, 10, 11, 12, 13, 14, 15, 18, ... 0.163601 \n","2062 (3837, ({3, 5, 6, 10, 12, 13, 14, 15, 23, 24, ... 0.090466 \n","2052 (3867, ({2, 3, 6, 7, 8, 9, 14, 16, 17, 19, 21,... 0.197926 \n","2070 (3764, ({0, 3, 5, 6, 8, 11, 14, 15, 16, 17, 20... 0.096126 \n","2068 (4123, ({0, 3, 7, 11, 15, 18, 20, 21, 22, 23, ... 0.112556 \n","2035 (3928, ({7, 9, 15, 16, 17, 18, 19, 20, 21, 22,... 0.148620 \n","2030 (4772, ({0, 3, 4, 6, 9, 10, 14, 15, 18, 21, 26... 0.095720 \n","2036 (4135, ({0, 1, 2, 3, 4, 6, 11, 12, 14, 15, 16,... 0.094568 \n","2033 (4556, ({0, 2, 3, 4, 7, 8, 9, 10, 14, 15, 16, ... 0.135981 \n","2029 (3789, ({3, 11, 12, 13, 14, 15, 20, 24, 26, 27... 0.091927 \n","2038 (4849, ({0, 7, 8, 9, 15, 18, 25, 28, 29, 30, 3... 0.130442 \n","2063 (4181, ({0, 1, 4, 5, 9, 10, 14, 15, 16, 17, 18... 0.088969 \n","2061 (4031, ({1, 2, 3, 8, 9, 10, 17, 18, 22, 23, 24... 0.165223 \n","2059 (3636, ({3, 9, 10, 11, 12, 14, 15, 18, 19, 22,... 0.172253 \n","2040 (3889, ({0, 2, 3, 7, 8, 13, 18, 19, 21, 22, 27... 0.223788 \n","2056 (4099, ({0, 1, 2, 4, 12, 13, 14, 15, 18, 19, 2... 0.152378 \n","2048 (3895, ({0, 4, 8, 14, 18, 19, 20, 25, 26, 28, ... 0.135606 \n","2073 (3707, ({3, 5, 6, 11, 12, 15, 18, 19, 21, 22, ... 0.322831 \n","2076 (4230, ({1, 2, 3, 8, 13, 18, 20, 21, 24, 30, 3... 0.194100 \n","2039 (4200, ({0, 1, 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4, 5, 7, 8, 12, 16, 18, 20, 22,... 0.167957 \n","2114 (4127, ({3, 4, 5, 6, 11, 12, 13, 15, 19, 22, 2... 0.170634 \n","2108 (4238, ({0, 1, 4, 6, 8, 9, 12, 15, 17, 18, 19,... 0.108218 \n","2104 (3716, ({1, 4, 5, 10, 11, 14, 16, 18, 19, 22, ... 0.133848 \n","2078 (4092, ({0, 4, 5, 8, 16, 18, 24, 27, 28, 29, 3... 0.145216 \n","2101 (3996, ({1, 12, 14, 17, 18, 20, 21, 25, 26, 28... 0.146249 \n","2110 (4339, ({0, 7, 8, 9, 10, 12, 13, 14, 15, 19, 2... 0.115877 \n","2081 (4052, ({3, 4, 10, 11, 14, 15, 20, 21, 23, 24,... 0.105837 \n","2087 (4691, ({1, 4, 5, 6, 8, 9, 10, 19, 20, 21, 22,... 0.082929 \n","2121 (3754, ({0, 1, 5, 6, 11, 13, 16, 17, 25, 27, 2... 0.104617 \n","2092 (4091, ({1, 2, 3, 4, 9, 10, 11, 14, 15, 18, 24... 0.283960 \n","2079 (4068, ({1, 2, 3, 4, 6, 11, 13, 16, 18, 19, 24... 0.156715 \n","2080 (3790, ({4, 5, 11, 12, 13, 16, 17, 19, 20, 21,... 0.159516 \n","2113 (3881, ({3, 4, 8, 10, 11, 15, 18, 19, 20, 21, ... 0.068795 \n","2094 (4005, ({1, 2, 4, 5, 11, 14, 15, 28, 29, 31, 3... 0.155930 \n","2112 (4293, ({2, 3, 6, 8, 15, 18, 19, 26, 28, 29, 3... 0.267370 \n","2091 (3824, ({0, 4, 6, 14, 15, 17, 18, 19, 24, 27, ... 0.137107 \n","2090 (3937, ({1, 2, 9, 11, 12, 13, 18, 20, 21, 27, ... 0.096388 \n","2105 (4116, ({0, 3, 6, 7, 8, 9, 11, 12, 14, 15, 16,... 0.251890 \n","2102 (4484, ({1, 2, 6, 7, 8, 15, 16, 18, 19, 20, 24... 0.178332 \n","2088 (3976, ({0, 1, 3, 5, 8, 19, 20, 22, 23, 24, 26... 0.189120 \n","2109 (3799, ({0, 2, 6, 10, 13, 14, 15, 19, 20, 21, ... 0.107239 \n","2084 (3792, ({8, 12, 13, 16, 18, 20, 21, 22, 23, 24... 0.146797 \n","2098 (3824, ({0, 1, 2, 3, 15, 18, 19, 22, 23, 24, 3... 0.284490 \n","2118 (3918, ({0, 1, 2, 3, 4, 5, 6, 13, 14, 15, 16, ... 0.248703 \n","2119 (4100, ({0, 6, 7, 10, 11, 12, 13, 14, 16, 18, ... 0.288838 \n","2115 (3913, ({6, 8, 10, 11, 12, 19, 20, 22, 23, 25,... 0.159700 \n","2086 (4006, ({0, 1, 4, 8, 11, 12, 13, 14, 15, 19, 2... 0.114559 \n","2124 (4257, ({7, 9, 10, 11, 12, 13, 14, 15, 22, 23,... 0.184865 \n","2100 (3779, ({3, 8, 9, 10, 11, 13, 15, 17, 19, 25, ... 0.127140 \n","2117 (4054, ({0, 3, 4, 5, 6, 9, 13, 16, 19, 24, 25,... 0.065422 \n","2103 (3805, ({0, 2, 9, 10, 11, 13, 15, 16, 18, 19, ... 0.200730 \n","2125 (5068, ({4, 5, 8, 9, 10, 11, 13, 15, 16, 17, 1... 0.098470 \n","2085 (4702, ({1, 3, 8, 9, 10, 11, 15, 20, 21, 26, 2... 0.123308 \n","2120 (4061, ({0, 1, 2, 4, 5, 8, 10, 17, 18, 19, 20,... 0.183078 \n","2097 (3859, ({1, 2, 4, 5, 10, 11, 14, 15, 19, 20, 2... 0.217280 \n","2089 (4279, ({3, 5, 6, 7, 8, 14, 18, 19, 22, 24, 31... 0.165969 \n","2107 (3871, ({1, 2, 3, 8, 10, 11, 12, 13, 14, 17, 2... 0.121288 \n","2106 (3730, ({2, 3, 8, 9, 10, 11, 12, 14, 17, 21, 2... 0.140315 \n","2095 (3944, ({2, 3, 9, 10, 13, 18, 20, 26, 27, 28, ... 0.173505 \n","2093 (4034, ({1, 2, 3, 4, 5, 6, 11, 12, 14, 15, 16,... 0.093789 \n","2083 (3956, ({0, 1, 6, 7, 8, 10, 11, 14, 19, 21, 23... 0.110303 \n","2122 (3736, ({0, 1, 3, 6, 11, 13, 14, 15, 16, 17, 2... 0.140170 \n","2111 (4173, ({0, 1, 2, 7, 11, 12, 13, 15, 18, 19, 2... 0.206448 \n","2082 (3883, ({0, 1, 10, 12, 13, 14, 15, 16, 18, 20,... 0.136860 \n","2126 (4151, ({4, 8, 9, 10, 11, 13, 14, 18, 19, 23, ... 0.283247 \n","2116 (4266, ({0, 2, 3, 7, 11, 12, 20, 21, 22, 24, 2... 0.218141 \n","2096 (4177, ({0, 1, 3, 9, 10, 11, 16, 17, 19, 20, 2... 0.148185 \n","2077 (3923, ({0, 1, 6, 12, 13, 14, 16, 17, 18, 19, ... 0.296090 \n","2123 (4977, ({0, 1, 2, 4, 5, 8, 9, 10, 11, 14, 16, ... 0.190179 \n","2148 (4644, ({6, 7, 9, 10, 11, 12, 18, 19, 20, 22, ... 0.095029 \n","2155 (4283, ({1, 2, 3, 6, 7, 8, 18, 20, 23, 25, 27,... 0.092492 \n","2130 (4550, ({0, 1, 3, 6, 8, 12, 13, 15, 17, 20, 28... 0.063627 \n","2171 (5102, ({0, 2, 6, 7, 10, 15, 17, 26, 27, 29, 3... 0.207743 \n","2129 (4911, ({0, 3, 7, 10, 12, 13, 14, 17, 18, 21, ... 0.051111 \n","2151 (4444, ({3, 11, 12, 13, 14, 17, 18, 19, 22, 23... 0.132957 \n","2145 (4054, ({6, 10, 13, 15, 16, 18, 19, 22, 23, 30... 0.163812 \n","2142 (4042, ({1, 2, 5, 7, 8, 9, 10, 16, 19, 21, 23,... 0.145655 \n","2156 (4172, ({0, 1, 2, 9, 11, 14, 15, 17, 19, 20, 2... 0.087038 \n","2143 (3994, ({1, 3, 6, 8, 9, 10, 18, 19, 21, 23, 26... 0.130747 \n","2167 (3789, ({0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 1... 0.174059 \n","2144 (4294, ({3, 5, 7, 8, 11, 12, 13, 15, 16, 17, 2... 0.123412 \n","2147 (4105, ({3, 4, 6, 7, 9, 10, 11, 12, 15, 16, 17... 0.074764 \n","2152 (4064, ({0, 1, 2, 5, 6, 11, 18, 19, 20, 21, 22... 0.071820 \n","2163 (3706, ({0, 3, 11, 12, 13, 16, 18, 19, 20, 21,... 0.140332 \n","2138 (4278, ({0, 1, 5, 6, 8, 10, 11, 12, 13, 16, 17... 0.107367 \n","2159 (4127, ({0, 3, 5, 8, 9, 10, 11, 13, 14, 19, 22... 0.155797 \n","2158 (4656, ({0, 3, 6, 8, 10, 20, 21, 26, 28, 29, 3... 0.226764 \n","2134 (4726, ({1, 3, 6, 8, 9, 10, 11, 18, 21, 25, 26... 0.094114 \n","2169 (4197, ({0, 7, 8, 9, 10, 14, 15, 16, 17, 19, 2... 0.075451 \n","2136 (4118, ({1, 2, 7, 8, 9, 10, 13, 14, 18, 19, 23... 0.228281 \n","2137 (3899, ({0, 1, 2, 5, 10, 11, 14, 20, 21, 23, 2... 0.068928 \n","2166 (3865, ({1, 3, 4, 12, 14, 15, 18, 20, 21, 27, ... 0.141106 \n","2170 (3691, ({0, 1, 6, 7, 9, 11, 15, 16, 17, 19, 20... 0.171143 \n","2128 (3761, ({4, 5, 6, 7, 9, 10, 12, 13, 15, 16, 17... 0.074140 \n","2149 (4467, ({3, 7, 8, 9, 10, 12, 13, 14, 15, 19, 2... 0.128428 \n","2172 (4368, ({0, 2, 7, 10, 11, 12, 13, 16, 17, 18, ... 0.240552 \n","2168 (3713, ({1, 2, 3, 8, 11, 13, 14, 17, 18, 20, 2... 0.087035 \n","2160 (4143, ({0, 1, 2, 3, 4, 5, 6, 13, 20, 22, 23, ... 0.147253 \n","2154 (4676, ({2, 9, 10, 12, 13, 14, 15, 16, 17, 18,... 0.090250 \n","2161 (4526, ({7, 8, 14, 15, 18, 21, 22, 23, 24, 25,... 0.091317 \n","2140 (5439, ({0, 3, 5, 13, 14, 16, 17, 20, 21, 23, ... 0.086789 \n","2164 (4027, ({2, 6, 7, 9, 10, 14, 15, 18, 20, 21, 2... 0.147243 \n","2165 (4310, ({7, 11, 12, 15, 17, 18, 20, 21, 27, 30... 0.122801 \n","2146 (4049, ({8, 9, 10, 11, 13, 15, 16, 17, 18, 19,... 0.100410 \n","2150 (4427, ({4, 5, 7, 8, 9, 14, 15, 22, 24, 28, 29... 0.190277 \n","2141 (3711, ({0, 3, 6, 9, 10, 14, 19, 26, 27, 28, 2... 0.125881 \n","2131 (4019, ({0, 2, 6, 8, 11, 12, 13, 15, 16, 18, 2... 0.114685 \n","2135 (4308, ({4, 5, 8, 11, 16, 19, 20, 21, 22, 23, ... 0.126276 \n","2127 (4278, ({0, 2, 4, 5, 9, 14, 15, 17, 18, 20, 21... 0.277971 \n","2132 (4514, ({0, 1, 2, 3, 6, 12, 16, 18, 19, 23, 27... 0.129167 \n","2162 (3877, ({0, 1, 2, 4, 11, 17, 18, 19, 21, 22, 2... 0.102685 \n","2157 (3941, ({1, 3, 5, 10, 11, 13, 14, 15, 18, 19, ... 0.133296 \n","2139 (4277, ({0, 1, 2, 4, 7, 10, 14, 16, 18, 19, 20... 0.180186 \n","2133 (4111, ({3, 5, 6, 9, 13, 15, 16, 17, 18, 19, 2... 0.127737 \n","2153 (4641, ({0, 1, 2, 4, 11, 12, 14, 15, 24, 25, 2... 0.062355 \n","\n"," Avg Shortest Path Length Asteroidal Triple Bridges Local Bridges \\\n","2019 1.437977 [104, 115, 128] False 0.0 \n","2024 1.448825 [80, 125, 134] False 0.0 \n","2022 1.438875 [39, 70, 131] False 0.0 \n","2015 1.497755 [29, 44, 0] False 0.0 \n","2025 1.441568 [100, 112, 0] False 0.0 \n","2017 1.416130 [20, 162, 128] False 0.0 \n","2010 1.447329 [39, 70, 131] False 0.0 \n","2020 1.446207 [39, 70, 0] False 0.0 \n","2026 1.471644 [20, 162, 1] False 0.0 \n","2023 1.467006 [39, 70, 0] False 0.0 \n","2001 1.488104 [39, 70, 97] False 0.0 \n","2018 1.468727 [100, 112, 129] False 0.0 \n","2007 1.454137 [20, 162, 2] False 0.0 \n","2002 1.411492 [20, 162, 0] False 0.0 \n","2009 1.437304 [20, 162, 0] False 0.0 \n","2016 1.464761 [20, 162, 10] False 0.0 \n","2006 1.380892 [63, 76, 0] False 0.0 \n","2003 1.425557 [80, 125, 1] False 0.0 \n","2008 1.411492 [63, 76, 129] False 0.0 \n","2014 1.446431 [20, 162, 64] False 0.0 \n","2021 1.496110 [20, 162, 2] False 0.0 \n","2004 1.452491 [39, 70, 130] False 0.0 \n","2011 1.430570 [20, 162, 6] False 0.0 \n","2005 1.443813 [20, 162, 128] False 0.0 \n","2012 1.269265 [68, 138, 39] False 0.0 \n","2042 1.455185 [39, 70, 0] False 0.0 \n","2044 1.478004 [20, 162, 5] False 0.0 \n","2013 1.480398 [80, 125, 129] False 0.0 \n","2067 1.479276 [39, 70, 0] False 0.0 \n","2062 1.471794 [80, 125, 4] False 0.0 \n","2052 1.469176 [39, 70, 128] False 0.0 \n","2070 1.484513 [20, 162, 128] False 0.0 \n","2068 1.431169 [20, 162, 132] False 0.0 \n","2035 1.458327 [20, 162, 5] False 0.0 \n","2030 1.331363 [50, 96, 7] False 0.0 \n","2036 1.428400 [20, 162, 97] False 0.0 \n","2033 1.368248 [20, 162, 6] False 0.0 \n","2029 1.480847 [20, 162, 98] False 0.0 \n","2038 1.324031 [20, 162, 99] False 0.0 \n","2063 1.427802 [20, 162, 128] False 0.0 \n","2061 1.441793 [20, 162, 0] False 0.0 \n","2059 1.500673 [20, 162, 0] False 0.0 \n","2040 1.470971 [63, 76, 128] False 0.0 \n","2056 1.438725 [20, 162, 132] False 0.0 \n","2048 1.462816 [20, 162, 131] False 0.0 \n","2073 1.488329 [20, 162, 0] False 0.0 \n","2076 1.411866 [20, 162, 129] False 0.0 \n","2039 1.416430 [20, 162, 129] False 0.0 \n","2051 1.445833 [100, 112, 3] False 0.0 \n","2049 1.479500 [20, 162, 130] False 0.0 \n","2075 1.354407 [68, 138, 0] False 0.0 \n","2043 1.463639 [20, 162, 3] False 0.0 \n","2069 1.455409 [57, 163, 129] False 0.0 \n","2027 1.429597 [39, 70, 0] False 0.0 \n","2074 1.483017 [20, 162, 0] False 0.0 \n","2058 1.415457 [20, 162, 129] False 0.0 \n","2055 1.444935 [20, 162, 1] False 0.0 \n","2065 1.444561 [20, 162, 32] False 0.0 \n","2053 1.452491 [20, 162, 0] False 0.0 \n","2046 1.413811 [20, 162, 34] False 0.0 \n","2072 1.396304 [63, 76, 0] False 0.0 \n","2034 1.350741 [68, 138, 129] False 0.0 \n","2041 1.354856 [49, 146, 141] False 0.0 \n","2057 1.437827 [39, 70, 131] False 0.0 \n","2031 1.501272 [39, 70, 131] False 0.0 \n","2066 1.497007 [20, 162, 131] False 0.0 \n","2064 1.436705 [20, 162, 6] False 0.0 \n","2032 1.454511 [20, 162, 129] False 0.0 \n","2054 1.458926 [100, 112, 1] False 0.0 \n","2071 1.436107 [29, 44, 136] False 0.0 \n","2060 1.455559 [20, 162, 128] False 0.0 \n","2028 1.390094 [20, 162, 129] False 0.0 \n","2045 1.444710 [67, 137, 2] False 0.0 \n","2050 1.458701 [80, 125, 6] False 0.0 \n","2047 1.458028 [20, 162, 131] False 0.0 \n","2037 1.468801 [20, 162, 0] False 0.0 \n","2099 1.444561 [39, 70, 97] False 0.0 \n","2114 1.430944 [20, 162, 0] False 0.0 \n","2108 1.413287 [20, 162, 0] False 0.0 \n","2104 1.484962 [80, 125, 128] False 0.0 \n","2078 1.437154 [20, 162, 0] False 0.0 \n","2101 1.440745 [63, 76, 129] False 0.0 \n","2110 1.406928 [20, 162, 97] False 0.0 \n","2081 1.441044 [20, 162, 0] False 0.0 \n","2087 1.342137 [14, 74, 159] False 0.0 \n","2121 1.479500 [20, 162, 130] False 0.0 \n","2092 1.434610 [80, 125, 129] False 0.0 \n","2079 1.437378 [20, 162, 0] False 0.0 \n","2080 1.472767 [39, 70, 0] False 0.0 \n","2113 1.461245 [80, 125, 130] False 0.0 \n","2094 1.446057 [20, 162, 0] False 0.0 \n","2112 1.406255 [20, 162, 133] False 0.0 \n","2091 1.468053 [20, 162, 4] False 0.0 \n","2090 1.460347 [39, 70, 4] False 0.0 \n","2105 1.432740 [20, 162, 1] False 0.0 \n","2102 1.379545 [20, 162, 129] False 0.0 \n","2088 1.457878 [20, 162, 129] False 0.0 \n","2109 1.478827 [20, 162, 0] False 0.0 \n","2084 1.478228 [20, 162, 0] False 0.0 \n","2098 1.470298 [20, 162, 3] False 0.0 \n","2118 1.464612 [39, 70, 131] False 0.0 \n","2119 1.428924 [20, 162, 132] False 0.0 \n","2115 1.456831 [20, 162, 129] False 0.0 \n","2086 1.445908 [20, 162, 129] False 0.0 \n","2124 1.414036 [20, 162, 129] False 0.0 \n","2100 1.481745 [20, 162, 0] False 0.0 \n","2117 1.440596 [20, 162, 1] False 0.0 \n","2103 1.474488 [20, 162, 1] False 0.0 \n","2125 1.288344 [68, 138, 2] False 0.0 \n","2085 1.343932 [147, 163, 0] False 0.0 \n","2120 1.438575 [29, 44, 128] False 0.0 \n","2097 1.475460 [20, 162, 1] False 0.0 \n","2089 1.405432 [20, 162, 7] False 0.0 \n","2107 1.473216 [20, 162, 0] False 0.0 \n","2106 1.491246 [20, 162, 1] False 0.0 \n","2095 1.453763 [100, 112, 0] False 0.0 \n","2093 1.440147 [20, 162, 7] False 0.0 \n","2083 1.451145 [80, 125, 161] False 0.0 \n","2122 1.483914 [20, 162, 0] False 0.0 \n","2111 1.424734 [20, 162, 4] False 0.0 \n","2082 1.467230 [20, 162, 0] False 0.0 \n","2126 1.429523 [39, 70, 43] False 0.0 \n","2116 1.404983 [20, 162, 129] False 0.0 \n","2096 1.420619 [20, 162, 4] False 0.0 \n","2077 1.460422 [29, 44, 129] False 0.0 \n","2123 1.307497 [68, 138, 129] False 0.0 \n","2148 1.344007 [50, 96, 163] False 0.0 \n","2155 1.402215 [20, 162, 0] False 0.0 \n","2130 1.367799 [20, 162, 140] False 0.0 \n","2171 1.282807 [22, 154, 96] False 0.0 \n","2129 1.317372 [50, 96, 18] False 0.0 \n","2151 1.384184 [100, 112, 162] False 0.0 \n","2145 1.434386 [20, 162, 1] False 0.0 \n","2142 1.439847 [20, 162, 2] False 0.0 \n","2156 1.423238 [20, 162, 135] False 0.0 \n","2143 1.445758 [20, 162, 128] False 0.0 \n","2167 1.473964 [39, 70, 0] False 0.0 \n","2144 1.409921 [100, 112, 2] False 0.0 \n","2147 1.431992 [20, 162, 130] False 0.0 \n","2152 1.437977 [20, 162, 97] False 0.0 \n","2163 1.488029 [20, 162, 131] False 0.0 \n","2138 1.396005 [20, 162, 0] False 0.0 \n","2159 1.430196 [39, 70, 129] False 0.0 \n","2158 1.349020 [49, 146, 0] False 0.0 \n","2134 1.332859 [75, 104, 129] False 0.0 \n","2169 1.418824 [20, 162, 131] False 0.0 \n","2136 1.436256 [20, 162, 132] False 0.0 \n","2137 1.459075 [20, 162, 6] False 0.0 \n","2166 1.468502 [20, 162, 128] False 0.0 \n","2170 1.491546 [20, 162, 131] False 0.0 \n","2128 1.483166 [20, 162, 0] False 0.0 \n","2149 1.380593 [20, 162, 35] False 0.0 \n","2172 1.397576 [20, 162, 0] False 0.0 \n","2168 1.492444 [20, 162, 130] False 0.0 \n","2160 1.431243 [100, 112, 159] False 0.0 \n","2154 1.355305 [147, 163, 0] False 0.0 \n","2161 1.372512 [20, 162, 163] False 0.0 \n","2140 1.237767 [68, 138, 162] False 0.0 \n","2164 1.444187 [20, 162, 130] False 0.0 \n","2165 1.403711 [20, 162, 133] False 0.0 \n","2146 1.440670 [20, 162, 128] False 0.0 \n","2150 1.387176 [20, 162, 0] False 0.0 \n","2141 1.492444 [20, 162, 128] False 0.0 \n","2131 1.442466 [20, 162, 5] False 0.0 \n","2135 1.395706 [20, 162, 131] False 0.0 \n","2127 1.410893 [29, 44, 129] False 0.0 \n","2132 1.367574 [50, 96, 68] False 0.0 \n","2162 1.457579 [100, 112, 0] False 0.0 \n","2157 1.451594 [39, 70, 0] False 0.0 \n","2139 1.408050 [20, 162, 135] False 0.0 \n","2133 1.434610 [20, 162, 1] False 0.0 \n","2153 1.360766 [50, 96, 163] False 0.0 \n","\n"," Graph colouring Avg Degree Global Clustering Edges Chordal \\\n","2019 49.0 45.804878 0.688333 7512.0 False \n","2024 43.0 44.920732 0.643601 7367.0 False \n","2022 42.0 45.731707 0.668338 7500.0 False \n","2015 44.0 40.932927 0.658575 6713.0 False \n","2025 42.0 45.512195 0.643546 7464.0 False \n","2017 45.0 47.585366 0.671961 7804.0 False \n","2010 45.0 45.042683 0.660352 7387.0 False \n","2020 40.0 45.134146 0.644929 7402.0 False \n","2026 41.0 43.060976 0.622604 7062.0 False \n","2023 38.0 43.439024 0.621843 7124.0 False \n","2001 40.0 41.719512 0.624067 6842.0 False \n","2018 45.0 43.298780 0.649441 7101.0 False \n","2007 43.0 44.487805 0.648795 7296.0 False \n","2002 51.0 47.963415 0.690387 7866.0 False \n","2009 46.0 45.859756 0.676030 7521.0 False \n","2016 41.0 43.621951 0.644739 7154.0 False \n","2006 48.0 50.457317 0.702655 8275.0 False \n","2003 44.0 46.817073 0.667762 7678.0 False \n","2008 52.0 47.963415 0.688201 7866.0 False \n","2014 44.0 45.115854 0.666603 7399.0 False \n","2021 38.0 41.067073 0.617040 6735.0 False \n","2004 43.0 44.621951 0.638818 7318.0 False \n","2011 45.0 46.408537 0.668854 7611.0 False \n","2005 45.0 45.329268 0.644864 7434.0 False \n","2012 71.0 59.554878 0.807532 9767.0 False \n","2042 41.0 44.402439 0.651236 7282.0 False \n","2044 50.0 42.542683 0.657188 6977.0 False \n","2013 42.0 42.347561 0.633101 6945.0 False \n","2067 41.0 42.439024 0.630545 6960.0 False \n","2062 42.0 43.048780 0.623979 7060.0 False \n","2052 43.0 43.262195 0.639916 7095.0 False \n","2070 43.0 42.012195 0.636653 6890.0 False \n","2068 51.0 46.359756 0.697440 7603.0 False \n","2035 47.0 44.146341 0.660729 7240.0 False \n","2030 61.0 54.493902 0.753845 8937.0 False \n","2036 42.0 46.585366 0.653785 7640.0 False \n","2033 54.0 51.487805 0.720692 8444.0 False \n","2029 42.0 42.310976 0.631969 6939.0 False \n","2038 69.0 55.091463 0.759686 9035.0 False \n","2063 51.0 46.634146 0.677373 7648.0 False \n","2061 44.0 45.493902 0.655389 7461.0 False \n","2059 38.0 40.695122 0.612250 6674.0 False \n","2040 49.0 43.115854 0.655452 7071.0 False \n","2056 45.0 45.743902 0.656577 7502.0 False \n","2048 41.0 43.780488 0.638660 7180.0 False \n","2073 50.0 41.701220 0.662090 6839.0 False \n","2076 49.0 47.932927 0.692870 7861.0 False \n","2039 48.0 47.560976 0.671663 7800.0 False \n","2051 55.0 45.164634 0.687429 7407.0 False \n","2049 45.0 42.420732 0.643667 6957.0 False \n","2075 53.0 52.615854 0.732850 8629.0 False \n","2043 44.0 43.713415 0.644545 7169.0 False \n","2069 46.0 44.384146 0.656334 7279.0 False \n","2027 44.0 46.487805 0.661009 7624.0 False \n","2074 43.0 42.134146 0.639270 6910.0 False \n","2058 48.0 47.640244 0.687553 7813.0 False \n","2055 48.0 45.237805 0.678727 7419.0 False \n","2065 46.0 45.268293 0.673326 7424.0 False \n","2053 41.0 44.621951 0.652324 7318.0 False \n","2046 52.0 47.774390 0.724110 7835.0 False \n","2072 45.0 49.201220 0.682544 8069.0 False \n","2034 52.0 52.914634 0.733150 8678.0 False \n","2041 68.0 52.579268 0.749408 8623.0 False \n","2057 45.0 45.817073 0.671073 7514.0 False \n","2031 40.0 40.646341 0.630619 6666.0 False \n","2066 41.0 40.993902 0.639779 6723.0 False \n","2064 43.0 45.908537 0.663743 7529.0 False \n","2032 43.0 44.457317 0.639628 7291.0 False \n","2054 48.0 44.097561 0.659846 7232.0 False \n","2071 59.0 45.957317 0.717209 7537.0 False \n","2060 38.0 44.371951 0.635333 7277.0 False \n","2028 56.0 49.707317 0.704491 8152.0 False \n","2045 45.0 45.256098 0.655559 7422.0 False \n","2050 41.0 44.115854 0.643761 7235.0 False \n","2047 48.0 44.170732 0.662248 7244.0 False \n","2037 42.0 43.292683 0.643106 7100.0 False \n","2099 41.0 45.268293 0.651451 7424.0 False \n","2114 43.0 46.378049 0.676270 7606.0 False \n","2108 47.0 47.817073 0.682713 7842.0 False \n","2104 35.0 41.975610 0.603081 6884.0 False \n","2078 44.0 45.871951 0.666233 7523.0 False \n","2101 42.0 45.579268 0.649698 7475.0 False \n","2110 49.0 48.335366 0.697148 7927.0 False \n","2081 44.0 45.554878 0.649283 7471.0 False \n","2087 53.0 53.615854 0.745867 8793.0 False \n","2121 37.0 42.420732 0.609117 6957.0 False \n","2092 52.0 46.079268 0.686550 7557.0 False \n","2079 40.0 45.853659 0.652411 7520.0 False \n","2080 39.0 42.969512 0.614164 7047.0 False \n","2113 40.0 43.908537 0.629540 7201.0 False \n","2094 45.0 45.146341 0.657482 7404.0 False \n","2112 56.0 48.390244 0.708464 7936.0 False \n","2091 40.0 43.353659 0.634064 7110.0 False \n","2090 42.0 43.981707 0.658532 7213.0 False \n","2105 50.0 46.231707 0.695584 7582.0 False \n","2102 58.0 50.567073 0.717028 8293.0 False \n","2088 47.0 44.182927 0.659866 7246.0 False \n","2109 40.0 42.475610 0.608554 6966.0 False \n","2084 41.0 42.524390 0.636794 6974.0 False \n","2098 42.0 43.170732 0.638049 7080.0 False \n","2118 57.0 43.634146 0.688296 7156.0 False \n","2119 48.0 46.542683 0.677374 7633.0 False \n","2115 43.0 44.268293 0.648416 7260.0 False \n","2086 42.0 45.158537 0.646073 7406.0 False \n","2124 51.0 47.756098 0.680836 7832.0 False \n","2100 42.0 42.237805 0.643532 6927.0 False \n","2117 41.0 45.591463 0.643955 7477.0 False \n","2103 39.0 42.829268 0.628162 7024.0 False \n","2125 64.0 58.000000 0.791042 9512.0 False \n","2085 54.0 53.469512 0.745651 8769.0 False \n","2120 46.0 45.756098 0.671936 7504.0 False \n","2097 40.0 42.750000 0.635379 7011.0 False \n","2089 51.0 48.457317 0.697522 7947.0 False \n","2107 43.0 42.932927 0.658542 7041.0 False \n","2106 40.0 41.463415 0.627432 6800.0 False \n","2095 41.0 44.518293 0.630176 7301.0 False \n","2093 52.0 45.628049 0.691681 7483.0 False \n","2083 44.0 44.731707 0.648111 7336.0 False \n","2122 41.0 42.060976 0.625860 6898.0 False \n","2111 51.0 46.884146 0.686283 7689.0 False \n","2082 44.0 43.420732 0.646613 7121.0 False \n","2126 52.0 46.493902 0.685836 7625.0 False \n","2116 50.0 48.493902 0.694035 7953.0 False \n","2096 50.0 47.219512 0.682315 7744.0 False \n","2077 47.0 43.975610 0.655128 7212.0 False \n","2123 73.0 56.439024 0.801971 9256.0 False \n","2148 55.0 53.463415 0.737253 8768.0 False \n","2155 49.0 48.719512 0.690353 7990.0 False \n","2130 49.0 51.524390 0.721335 8450.0 False \n","2171 74.0 58.451220 0.801687 9586.0 False \n","2129 57.0 55.634146 0.769762 9124.0 False \n","2151 52.0 50.189024 0.707942 8231.0 False \n","2145 47.0 46.097561 0.665029 7560.0 False \n","2142 52.0 45.652439 0.682807 7487.0 False \n","2156 53.0 47.006098 0.692605 7709.0 False \n","2143 41.0 45.170732 0.659991 7408.0 False \n","2167 41.0 42.871951 0.636250 7031.0 False \n","2144 48.0 48.091463 0.687510 7887.0 False \n","2147 45.0 46.292683 0.653596 7592.0 False \n","2152 42.0 45.804878 0.669312 7512.0 False \n","2163 42.0 41.725610 0.635558 6843.0 False \n","2138 54.0 49.225610 0.710150 8073.0 False \n","2159 46.0 46.439024 0.664014 7616.0 False \n","2158 65.0 53.054878 0.755375 8701.0 False \n","2134 54.0 54.371951 0.741354 8917.0 False \n","2169 53.0 47.365854 0.680857 7768.0 False \n","2136 54.0 45.945122 0.675731 7535.0 False \n","2137 43.0 44.085366 0.638338 7230.0 False \n","2166 45.0 43.317073 0.654430 7104.0 False \n","2170 39.0 41.439024 0.619671 6796.0 False \n","2128 46.0 42.121951 0.653026 6908.0 False \n","2149 52.0 50.481707 0.724212 8279.0 False \n","2172 60.0 49.097561 0.713557 8052.0 False \n","2168 40.0 41.365854 0.632316 6784.0 False \n","2160 44.0 46.353659 0.671636 7602.0 False \n","2154 59.0 52.542683 0.739034 8617.0 False \n","2161 55.0 51.140244 0.723521 8387.0 False \n","2140 72.0 62.121951 0.832469 10188.0 False \n","2164 42.0 45.298780 0.631140 7429.0 False \n","2165 54.0 48.597561 0.704138 7970.0 False \n","2146 43.0 45.585366 0.652785 7476.0 False \n","2150 55.0 49.945122 0.705228 8191.0 False \n","2141 38.0 41.365854 0.615066 6784.0 False \n","2131 41.0 45.439024 0.645399 7452.0 False \n","2135 46.0 49.250000 0.689159 8077.0 False \n","2127 60.0 48.012195 0.719480 7874.0 False \n","2132 49.0 51.542683 0.709857 8453.0 False \n","2162 40.0 44.207317 0.637452 7250.0 False \n","2157 45.0 44.695122 0.655512 7330.0 False \n","2139 49.0 48.243902 0.701528 7912.0 False \n","2133 47.0 46.079268 0.671572 7557.0 False \n","2153 54.0 52.097561 0.721741 8544.0 False \n","\n"," Maximal Cliques Num of isolates Non Randomness wrt Random Model \\\n","2019 227045.0 0.0 7.277249 \n","2024 165809.0 0.0 2.495979 \n","2022 261112.0 0.0 3.893600 \n","2015 33730.0 0.0 0.766125 \n","2025 289857.0 0.0 2.706520 \n","2017 465583.0 0.0 3.686776 \n","2010 340624.0 0.0 5.674585 \n","2020 433172.0 0.0 3.632726 \n","2026 140155.0 0.0 1.790843 \n","2023 170074.0 0.0 1.953470 \n","2001 95316.0 0.0 1.295260 \n","2018 85479.0 0.0 3.749277 \n","2007 127133.0 0.0 3.019981 \n","2002 316538.0 0.0 4.475254 \n","2009 118837.0 0.0 4.519213 \n","2016 132992.0 0.0 2.386453 \n","2006 514570.0 0.0 3.719736 \n","2003 632171.0 0.0 4.071428 \n","2008 430027.0 0.0 4.457034 \n","2014 209043.0 0.0 2.742011 \n","2021 59676.0 0.0 0.696142 \n","2004 221252.0 0.0 3.730499 \n","2011 293623.0 0.0 2.985657 \n","2005 211212.0 0.0 2.735188 \n","2012 858989.0 0.0 8.424471 \n","2042 212400.0 0.0 3.483528 \n","2044 68496.0 0.0 3.707790 \n","2013 116355.0 0.0 1.612991 \n","2067 163839.0 0.0 2.247327 \n","2062 155845.0 0.0 1.011585 \n","2052 144546.0 0.0 3.482125 \n","2070 70742.0 0.0 1.591885 \n","2068 163109.0 0.0 3.458729 \n","2035 140215.0 0.0 2.739114 \n","2030 1281881.0 0.0 6.064478 \n","2036 409071.0 0.0 3.246370 \n","2033 859669.0 0.0 5.606039 \n","2029 80910.0 0.0 1.276170 \n","2038 555722.0 0.0 6.167336 \n","2063 254206.0 0.0 2.494494 \n","2061 220342.0 0.0 3.336317 \n","2059 72659.0 0.0 1.245983 \n","2040 53847.0 0.0 2.839933 \n","2056 152743.0 0.0 3.209659 \n","2048 123199.0 0.0 2.392270 \n","2073 33981.0 0.0 3.526566 \n","2076 713564.0 0.0 5.639553 \n","2039 365371.0 0.0 2.854819 \n","2051 89104.0 0.0 4.653854 \n","2049 56835.0 0.0 1.334603 \n","2075 1501073.0 0.0 5.217935 \n","2043 122028.0 0.0 1.510342 \n","2069 125518.0 0.0 4.412146 \n","2027 402498.0 0.0 2.668836 \n","2074 90166.0 0.0 1.044081 \n","2058 347615.0 0.0 4.766550 \n","2055 105832.0 0.0 4.250403 \n","2065 199950.0 0.0 5.733721 \n","2053 120042.0 0.0 2.220581 \n","2046 188814.0 0.0 4.185537 \n","2072 429935.0 0.0 3.363692 \n","2034 782138.0 0.0 5.880217 \n","2041 177544.0 0.0 8.766873 \n","2057 345661.0 0.0 3.435442 \n","2031 35359.0 0.0 1.261431 \n","2066 46130.0 0.0 3.007564 \n","2064 246927.0 0.0 3.919790 \n","2032 160154.0 0.0 1.631310 \n","2054 139667.0 0.0 4.410228 \n","2071 56794.0 0.0 6.709588 \n","2060 287709.0 0.0 2.406804 \n","2028 652462.0 0.0 4.666857 \n","2045 211170.0 0.0 2.359846 \n","2050 159427.0 0.0 4.004547 \n","2047 79734.0 0.0 3.005112 \n","2037 88192.0 0.0 1.869529 \n","2099 207727.0 0.0 3.212866 \n","2114 218348.0 0.0 5.413105 \n","2108 578662.0 0.0 4.078344 \n","2104 142090.0 0.0 1.613855 \n","2078 215845.0 0.0 3.176003 \n","2101 315302.0 0.0 2.918129 \n","2110 319155.0 0.0 4.664130 \n","2081 171091.0 0.0 2.221713 \n","2087 708021.0 0.0 6.050365 \n","2121 122983.0 0.0 1.182001 \n","2092 153346.0 0.0 6.797186 \n","2079 421656.0 0.0 3.917581 \n","2080 231488.0 0.0 2.351485 \n","2113 171512.0 0.0 1.888365 \n","2094 176455.0 0.0 3.093169 \n","2112 364955.0 0.0 6.399297 \n","2091 119134.0 0.0 2.373193 \n","2090 133572.0 0.0 2.796470 \n","2105 295818.0 0.0 5.097281 \n","2102 240345.0 0.0 4.878189 \n","2088 156268.0 0.0 3.480570 \n","2109 156976.0 0.0 1.319435 \n","2084 103429.0 0.0 1.878297 \n","2098 273458.0 0.0 3.652899 \n","2118 43786.0 0.0 2.808971 \n","2119 722357.0 0.0 6.837325 \n","2115 141771.0 0.0 3.293832 \n","2086 243223.0 0.0 2.318802 \n","2124 320427.0 0.0 3.693268 \n","2100 58866.0 0.0 1.090085 \n","2117 215025.0 0.0 1.386209 \n","2103 125811.0 0.0 3.471587 \n","2125 2320148.0 0.0 6.933309 \n","2085 428540.0 0.0 6.154509 \n","2120 183908.0 0.0 4.208764 \n","2097 144473.0 0.0 3.377103 \n","2089 425633.0 0.0 6.750310 \n","2107 67466.0 0.0 2.126253 \n","2106 61692.0 0.0 2.230034 \n","2095 217990.0 0.0 2.212138 \n","2093 112874.0 0.0 2.991557 \n","2083 130975.0 0.0 1.806311 \n","2122 96165.0 0.0 1.538825 \n","2111 145085.0 0.0 5.252105 \n","2082 115355.0 0.0 2.526843 \n","2126 107196.0 0.0 5.574138 \n","2116 384635.0 0.0 4.567058 \n","2096 177187.0 0.0 4.098318 \n","2077 145832.0 0.0 5.008029 \n","2123 96423.0 0.0 10.283087 \n","2148 2080923.0 0.0 5.945300 \n","2155 361951.0 0.0 3.273859 \n","2130 1070303.0 0.0 3.784354 \n","2171 569048.0 0.0 9.688356 \n","2129 1239348.0 0.0 5.273559 \n","2151 787695.0 0.0 5.404443 \n","2145 261278.0 0.0 4.162184 \n","2142 123487.0 0.0 2.815621 \n","2156 353125.0 0.0 3.369520 \n","2143 152155.0 0.0 3.386302 \n","2167 111904.0 0.0 2.366976 \n","2144 264418.0 0.0 4.055285 \n","2147 348136.0 0.0 2.482218 \n","2152 205366.0 0.0 3.166093 \n","2163 70475.0 0.0 2.094016 \n","2138 299068.0 0.0 4.345153 \n","2159 176275.0 0.0 3.432622 \n","2158 317337.0 0.0 9.917683 \n","2134 1191976.0 0.0 5.595349 \n","2169 264877.0 0.0 2.512403 \n","2136 112822.0 0.0 4.545361 \n","2137 147201.0 0.0 1.783841 \n","2166 94333.0 0.0 2.985451 \n","2170 70158.0 0.0 1.489397 \n","2128 84787.0 0.0 1.193266 \n","2149 670035.0 0.0 5.383133 \n","2172 199819.0 0.0 5.821490 \n","2168 58397.0 0.0 0.765920 \n","2160 233941.0 0.0 4.075216 \n","2154 365724.0 0.0 4.986322 \n","2161 769793.0 0.0 3.770685 \n","2140 1913292.0 0.0 7.227305 \n","2164 232616.0 0.0 2.774070 \n","2165 271287.0 0.0 3.999058 \n","2146 271408.0 0.0 2.036711 \n","2150 340530.0 0.0 5.762098 \n","2141 93882.0 0.0 1.312934 \n","2131 216226.0 0.0 1.977011 \n","2135 480536.0 0.0 3.862467 \n","2127 187173.0 0.0 7.058629 \n","2132 1275388.0 0.0 5.262627 \n","2162 229522.0 0.0 2.672876 \n","2157 178971.0 0.0 1.901956 \n","2139 481345.0 0.0 5.175136 \n","2133 169682.0 0.0 3.187179 \n","2153 592404.0 0.0 3.848097 \n","\n"," Transitivity Connected Components Diameter 1 Edge Connected \\\n","2019 0.698336 1.0 2.0 True \n","2024 0.644565 1.0 2.0 True \n","2022 0.666596 1.0 2.0 True \n","2015 0.652857 1.0 2.0 True \n","2025 0.640787 1.0 2.0 True \n","2017 0.672450 1.0 2.0 True \n","2010 0.664132 1.0 2.0 True \n","2020 0.645652 1.0 2.0 True \n","2026 0.618605 1.0 2.0 True \n","2023 0.621398 1.0 2.0 True \n","2001 0.619708 1.0 2.0 True \n","2018 0.653283 1.0 2.0 True \n","2007 0.648262 1.0 2.0 True \n","2002 0.688748 1.0 2.0 True \n","2009 0.677979 1.0 2.0 True \n","2016 0.641166 1.0 2.0 True \n","2006 0.698530 1.0 2.0 True \n","2003 0.665443 1.0 2.0 True \n","2008 0.687060 1.0 2.0 True \n","2014 0.660747 1.0 2.0 True \n","2021 0.614149 1.0 2.0 True \n","2004 0.640309 1.0 2.0 True \n","2011 0.664580 1.0 2.0 True \n","2005 0.644686 1.0 2.0 True \n","2012 0.816065 1.0 2.0 True \n","2042 0.649907 1.0 2.0 True \n","2044 0.656986 1.0 2.0 True \n","2013 0.629158 1.0 2.0 True \n","2067 0.628454 1.0 2.0 True \n","2062 0.621167 1.0 2.0 True \n","2052 0.641359 1.0 2.0 True \n","2070 0.631683 1.0 2.0 True \n","2068 0.689284 1.0 2.0 True \n","2035 0.657446 1.0 2.0 True \n","2030 0.753239 1.0 2.0 True \n","2036 0.652370 1.0 2.0 True \n","2033 0.721608 1.0 2.0 True \n","2029 0.628128 1.0 2.0 True \n","2038 0.761351 1.0 2.0 True \n","2063 0.672600 1.0 2.0 True \n","2061 0.656424 1.0 2.0 True \n","2059 0.611132 1.0 2.0 True \n","2040 0.656033 1.0 2.0 True \n","2056 0.656266 1.0 2.0 True \n","2048 0.637142 1.0 2.0 True \n","2073 0.664195 1.0 2.0 True \n","2076 0.695803 1.0 2.0 True \n","2039 0.670414 1.0 2.0 True \n","2051 0.684771 1.0 2.0 True \n","2049 0.642317 1.0 2.0 True \n","2075 0.730167 1.0 2.0 True \n","2043 0.640026 1.0 2.0 True \n","2069 0.662022 1.0 2.0 True \n","2027 0.659450 1.0 2.0 True \n","2074 0.631867 1.0 2.0 True \n","2058 0.685572 1.0 2.0 True \n","2055 0.678334 1.0 2.0 True \n","2065 0.674039 1.0 2.0 True \n","2053 0.651945 1.0 2.0 True \n","2046 0.711776 1.0 2.0 True \n","2072 0.681441 1.0 2.0 True \n","2034 0.734675 1.0 2.0 True \n","2041 0.762173 1.0 2.0 True \n","2057 0.665554 1.0 2.0 True \n","2031 0.630856 1.0 2.0 True \n","2066 0.641453 1.0 2.0 True 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"]},"execution_count":34,"metadata":{},"output_type":"execute_result"}],"source":["pd.set_option('display.max_rows', None)\n","pd.set_option('display.max_columns', None)\n","df"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true},"id":"Zukn6ABDxGxI"},"outputs":[],"source":[]}],"metadata":{"colab":{"provenance":[]},"gpuClass":"standard","kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/1. Feature Generation/Global Weighted Measures.ipynb b/Code/1. Feature Generation/Global Weighted Measures.ipynb new file mode 100644 index 0000000..6b6d0a2 --- /dev/null +++ b/Code/1. Feature Generation/Global Weighted Measures.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"UjuoxCJkdFyB","outputId":"5e97cb45-69b0-4766-9b8b-8f44498a2e6e"},"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9sfdMxAadg3P"},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","import networkx as nx\n","import os\n","import matplotlib.pyplot as plt\n","import graphviz\n","from operator import itemgetter\n","from networkx.algorithms import approximation as approx\n","from networkx.algorithms import bipartite"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":424},"id":"lME-Qk9jFK4f","outputId":"7dbfe664-ee2b-4ce2-908a-272b66483297"},"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Label\n","0 40013 0\n","1 40014 0\n","2 40017 0\n","3 40018 0\n","4 40019 0\n",".. ... ...\n","759 4167 0\n","760 4168 0\n","761 4169 1\n","762 4170 1\n","763 4171 1\n","\n","[764 rows x 2 columns]"],"text/html":["\n","
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v2'"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"QViH2nD4FU9Y","outputId":"3d51c68b-c30f-4423-eca2-fb21c55803a3"},"outputs":[{"output_type":"stream","name":"stdout","text":["171\n","3000\n","3010\n","3002\n","3009\n","3001\n","3006\n","3005\n","3003\n","3004\n","3007\n","3008\n","3011\n","3014\n","3013\n","3017\n","3016\n","3018\n","3012\n","3015\n","3019\n","3020\n","3021\n","3024\n","3023\n","3026\n","3025\n","3027\n","3028\n","3022\n","3030\n","3029\n","3031\n","3039\n","3038\n","3032\n","3036\n","3034\n","3035\n","3033\n","3037\n","3040\n","3041\n","3043\n","3042\n","3045\n","3046\n","3044\n","3047\n","3048\n","3050\n","3049\n","3051\n","3055\n","3054\n","3052\n","3053\n","3056\n","3057\n","3058\n","3059\n","3060\n","3061\n","3062\n","3063\n","3064\n","3069\n","3068\n","3070\n","3065\n","3067\n","3066\n","3071\n","3072\n","3073\n","3076\n","3074\n","3075\n","3079\n","3078\n","3081\n","3077\n","3080\n","3082\n","3084\n","3085\n","3083\n","3086\n","3091\n","3089\n","3088\n","3090\n","3087\n","3093\n","3096\n","3092\n","3095\n","3094\n","3099\n","3100\n","3097\n","3098\n","3101\n","3104\n","3103\n","3102\n","3105\n","3106\n","3110\n","3107\n","3109\n","3108\n","3111\n","3112\n","3113\n","3116\n","3115\n","3114\n","3119\n","3118\n","3121\n","3120\n","3117\n","3122\n","3123\n","3125\n","3126\n","3124\n","3129\n","3128\n","3130\n","3131\n","3133\n","3132\n","3135\n","3134\n","3136\n","3138\n","3137\n","3140\n","3139\n","3141\n","3142\n","3144\n","3143\n","3145\n","3146\n","3148\n","3149\n","3147\n","3150\n","3151\n","3152\n","3155\n","3154\n","3153\n","3156\n","3158\n","3161\n","3160\n","3159\n","3157\n","3162\n","3163\n","3164\n","3165\n","3166\n","3171\n","3168\n","3170\n","3167\n","3169\n"]}],"source":["# Add the directories as per requirement\n","dirs = [ub]\n","\n","graphs = list()\n","labels = list()\n","\n","for dir in dirs:\n"," for file in os.listdir(dir):\n"," if file.endswith(\".csv\"):\n"," if (dir == ub):\n"," subject = file[12:16]\n"," elif (dir == uw):\n"," subject = file[14:18]\n"," else:\n"," print(\"If you are using a statically binarized folder:\")\n"," print(\"Add a condition along with cb condition for COBRE and ub condition for UCLA\")\n"," print(\"Example: elif (dir == ub) becomes elif (dir == ub) or (dir == ub0_3)\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," mask = labels_mappings['Subject'] == int(subject)\n"," labels.append((labels_mappings[mask]['Label'].values[0], int(subject)))\n","\n"," # APPENDING CORRESPONDING GRAPH - may change based on implementation\n"," df = pd.read_csv(dir+file, header=None)\n"," G = nx.from_pandas_adjacency(df)\n"," graphs.append(G) "]},{"cell_type":"markdown","metadata":{"id":"_CltO0qDGdMd"},"source":["# Utility Function "]},{"cell_type":"code","execution_count":null,"metadata":{"id":"SmCnOLKoGgLy"},"outputs":[],"source":["class global_measures_weighted:\n","\n"," def __init__(self, subject_no, schiz, G, df):\n"," self.G = G\n"," self.subject = subject_no\n"," if schiz:\n"," self.schiz = 'Schizophrenic'\n"," else:\n"," self.schiz = 'Control'\n"," self.df = df\n"," self.df.at[self.subject, \"Subject\"] = int(self.subject)\n"," self.df.at[self.subject, \"Schizophrenic\"] = schiz\n"," \n"," print(\"\\nsubject \" + str(subject_no))\n"," \n"," self.average_shortest_path_length()\n"," self.stoer_wagner()\n"," self.wiener_index()\n"," self.dijkstra_path()\n"," self.max_weight_matching()\n"," self.cut_size()\n"," self.conductance() \n"," self.approx_randomized_partitioning()\n","\n"," def average_shortest_path_length(self): \n"," try:\n"," r = nx.average_shortest_path_length(self.G, weight='weight')\n"," except:\n"," r = 0\n"," self.df.at[self.subject, \"Average shortest path\"] = r\n","\n"," def stoer_wagner(self):\n"," try:\n"," cut, partition = nx.stoer_wagner(self.G, weight='weight')\n"," except: \n"," r = 0\n"," self.df.at[self.subject, \"Stoer Wagner cuts\"] = cut\n"," \n"," def wiener_index(self):\n"," try:\n"," r = nx.wiener_index(self.G, weight='weight')\n"," except:\n"," r = 0\n"," self.df.at[self.subject, \"Wiener Index\"] = r\n"," \n"," def dijkstra_path(self):\n"," try:\n"," r = nx.dijkstra_path(self.G, 0, 160, weight='weight')\n"," except: \n"," r = list()\n"," self.df.at[self.subject, \"Dijkstra path\"] = len(r)\n","\n"," def max_weight_matching(self):\n"," try:\n"," r = nx.max_weight_matching(self.G, maxcardinality=False, weight='weight')\n"," except: \n"," r = list()\n"," self.df.at[self.subject, \"Max weight matching\"] = len(r)\n","\n"," def barycenter(self):\n"," try:\n"," r = nx.barycenter(self.G, weight='weight', attr=None, sp=None)\n"," except:\n"," r = 0\n"," self.df.at[self.subject, \"Barycenter\"] = r\n","\n"," def cut_size(self):\n"," S = {0, 1, 2, 3}\n"," try:\n"," r = nx.cut_size(self.G,S, weight='weight')\n"," except:\n"," r = 0\n"," self.df.at[self.subject, \"Conductance\"] = r\n","\n"," def conductance(self):\n"," S = list(range(82))\n"," try:\n"," r = nx.conductance(self.G, S, T=None, weight='weight')\n"," except:\n"," r = 0\n"," self.df.at[self.subject, \"Conductance\"] = r\n","\n"," def approx_randomized_partitioning(self):\n"," try:\n"," r = approx.randomized_partitioning(self.G, seed=None, p=0.5, weight='weight')\n"," except:\n"," r = \"\"\n"," self.df.at[self.subject, \"Randomized Partitioning Heuristic\"] = str(r)\n"]},{"cell_type":"markdown","metadata":{"id":"OPq4EjM3IO_k"},"source":["# Driver function"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"s6bY2CryIMbZ","outputId":"b8830423-94fd-4f2a-83a4-d5044ea751d5"},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","subject 4018\n","\n","subject 4000\n","\n","subject 4016\n","\n","subject 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4071\n","\n","subject 4033\n","\n","subject 4042\n","\n","subject 4074\n","\n","subject 4045\n","\n","subject 4052\n","\n","subject 4026\n","\n","subject 4057\n","\n","subject 4073\n","\n","subject 4030\n","\n","subject 4048\n","\n","subject 4040\n","\n","subject 4050\n","\n","subject 4068\n","\n","subject 4064\n","\n","subject 4054\n","\n","subject 4063\n","\n","subject 4046\n","\n","subject 4065\n","\n","subject 4031\n","\n","subject 4103\n","\n","subject 4080\n","\n","subject 4113\n","\n","subject 4098\n","\n","subject 4044\n","\n","subject 4109\n","\n","subject 4027\n","\n","subject 4036\n","\n","subject 4070\n","\n","subject 4053\n","\n","subject 4059\n","\n","subject 4100\n","\n","subject 4049\n","\n","subject 4077\n","\n","subject 4107\n","\n","subject 4120\n","\n","subject 4056\n","\n","subject 4086\n","\n","subject 4111\n","\n","subject 4090\n","\n","subject 4088\n","\n","subject 4087\n","\n","subject 4106\n","\n","subject 4096\n","\n","subject 4097\n","\n","subject 4124\n","\n","subject 4079\n","\n","subject 4108\n","\n","subject 4078\n","\n","subject 4118\n","\n","subject 4104\n","\n","subject 4099\n","\n","subject 4119\n","\n","subject 4101\n","\n","subject 4116\n","\n","subject 4117\n","\n","subject 4112\n","\n","subject 4102\n","\n","subject 4084\n","\n","subject 4123\n","\n","subject 4083\n","\n","subject 4091\n","\n","subject 4089\n","\n","subject 4093\n","\n","subject 4085\n","\n","subject 4114\n","\n","subject 4141\n","\n","subject 4128\n","\n","subject 4170\n","\n","subject 4142\n","\n","subject 4129\n","\n","subject 4166\n","\n","subject 4147\n","\n","subject 4122\n","\n","subject 4076\n","\n","subject 4143\n","\n","subject 4155\n","\n","subject 4121\n","\n","subject 4081\n","\n","subject 4115\n","\n","subject 4110\n","\n","subject 4094\n","\n","subject 4105\n","\n","subject 4150\n","\n","subject 4154\n","\n","subject 4144\n","\n","subject 4125\n","\n","subject 4082\n","\n","subject 4095\n","\n","subject 4092\n","\n","subject 4163\n","\n","subject 4127\n","\n","subject 4165\n","\n","subject 4133\n","\n","subject 4162\n","\n","subject 4140\n","\n","subject 4151\n","\n","subject 4159\n","\n","subject 4146\n","\n","subject 4164\n","\n","subject 4148\n","\n","subject 4135\n","\n","subject 4137\n","\n","subject 4169\n","\n","subject 4153\n","\n","subject 4139\n","\n","subject 4136\n","\n","subject 4171\n","\n","subject 4167\n","\n","subject 4145\n","\n","subject 4160\n","\n","subject 4157\n","\n","subject 4158\n","\n","subject 4168\n","\n","subject 4149\n","\n","subject 4130\n","\n","subject 4126\n","\n","subject 4132\n","\n","subject 4152\n","\n","subject 4161\n","\n","subject 4138\n","\n","subject 4131\n","\n","subject 4156\n","\n","subject 4134\n"]}],"source":["output_df = pd.DataFrame(columns=['Subject', 'Schizophrenic'])\n","schiz=0\n","for i, g in enumerate(graphs):\n"," if(labels[i] > 4122):\n"," schiz =1\n"," global_measures_weighted(labels[i], schiz, g, output_df)"]},{"cell_type":"code","source":["output_df.to_csv('global_measures_weighted.csv')"],"metadata":{"id":"q4eueHWH4VDB"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Results"],"metadata":{"id":"DAy2EfCkhKuH"}},{"cell_type":"code","source":["output_df"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":676},"id":"hHlB7PyvtGyp","outputId":"3d2b9d54-dbac-4ebd-d9a5-a7eec537f624"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Schizophrenic Average shortest path Stoer Wagner cuts \\\n","3000 3000 0 0.012555 20.479361 \n","3010 3010 0 0.012412 16.898351 \n","3002 3002 0 0.010298 20.075623 \n","3009 3009 0 0.010249 22.489461 \n","3001 3001 0 0.009900 18.636786 \n","... ... ... ... ... \n","3171 3171 1 0.011135 18.207614 \n","3168 3168 1 0.010344 21.208409 \n","3170 3170 1 0.012029 25.750936 \n","3167 3167 1 0.009766 21.030312 \n","3169 3169 1 0.010490 19.338868 \n","\n"," Wiener Index Dijkstra path Max weight matching Conductance \\\n","3000 167.807115 6.0 82.0 0.495620 \n","3010 165.892491 8.0 82.0 0.498204 \n","3002 137.648029 8.0 82.0 0.491145 \n","3009 136.991810 4.0 82.0 0.472525 \n","3001 132.329467 7.0 82.0 0.497004 \n","... ... ... ... ... \n","3171 148.831164 7.0 82.0 0.504037 \n","3168 138.256592 4.0 82.0 0.485365 \n","3170 160.775121 4.0 82.0 0.496349 \n","3167 130.530521 7.0 82.0 0.508939 \n","3169 140.209955 5.0 82.0 0.497514 \n","\n"," Randomized Partitioning Heuristic \n","3000 (1648.6063707380802, ({0, 3, 4, 9, 12, 15, 16,... \n","3010 (1539.5217418635789, ({0, 128, 3, 132, 5, 6, 1... \n","3002 (1374.510072904605, ({1, 4, 6, 7, 14, 16, 18, ... \n","3009 (1412.5937324993017, ({2, 3, 4, 5, 6, 8, 14, 1... \n","3001 (1307.7308541961775, ({128, 129, 6, 7, 8, 9, 1... \n","... ... \n","3171 (1488.015140906703, ({6, 8, 10, 11, 12, 14, 15... \n","3168 (1401.7140954226836, ({0, 1, 3, 5, 6, 7, 8, 9,... \n","3170 (1642.0291251558797, ({4, 5, 6, 9, 11, 15, 20,... \n","3167 (1363.3718401436267, ({1, 4, 6, 12, 14, 15, 16... \n","3169 (1486.6317208546427, ({0, 2, 3, 4, 5, 6, 8, 14... \n","\n","[172 rows x 9 columns]"],"text/html":["\n","
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SubjectSchizophrenicAverage shortest pathStoer Wagner cutsWiener IndexDijkstra pathMax weight matchingConductanceRandomized Partitioning Heuristic
3000300000.01255520.479361167.8071156.082.00.495620(1648.6063707380802, ({0, 3, 4, 9, 12, 15, 16,...
3010301000.01241216.898351165.8924918.082.00.498204(1539.5217418635789, ({0, 128, 3, 132, 5, 6, 1...
3002300200.01029820.075623137.6480298.082.00.491145(1374.510072904605, ({1, 4, 6, 7, 14, 16, 18, ...
3009300900.01024922.489461136.9918104.082.00.472525(1412.5937324993017, ({2, 3, 4, 5, 6, 8, 14, 1...
3001300100.00990018.636786132.3294677.082.00.497004(1307.7308541961775, ({128, 129, 6, 7, 8, 9, 1...
..............................
3171317110.01113518.207614148.8311647.082.00.504037(1488.015140906703, ({6, 8, 10, 11, 12, 14, 15...
3168316810.01034421.208409138.2565924.082.00.485365(1401.7140954226836, ({0, 1, 3, 5, 6, 7, 8, 9,...
3170317010.01202925.750936160.7751214.082.00.496349(1642.0291251558797, ({4, 5, 6, 9, 11, 15, 20,...
3167316710.00976621.030312130.5305217.082.00.508939(1363.3718401436267, ({1, 4, 6, 12, 14, 15, 16...
3169316910.01049019.338868140.2099555.082.00.497514(1486.6317208546427, ({0, 2, 3, 4, 5, 6, 8, 14...
\n","

172 rows × 9 columns

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\n"," \n"," \n"," \n","\n"," \n","
\n","
\n"," "]},"metadata":{},"execution_count":27}]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/1. Feature Generation/Local Binary Measures.ipynb b/Code/1. Feature Generation/Local Binary Measures.ipynb new file mode 100644 index 0000000..d14b7ad --- /dev/null +++ b/Code/1. Feature Generation/Local Binary Measures.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","metadata":{"id":"Z8iIRE92FCxr"},"source":["# Import statements"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"PqrF5hQ1TumS","outputId":"3c52f693-5508-4291-a648-9ccd6a6e4e95"},"outputs":[{"name":"stdout","output_type":"stream","text":["Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OXjAAcZCdaPk"},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","import graphviz\n","import community\n","from operator import itemgetter\n","from google.colab import files\n","import os"]},{"cell_type":"markdown","metadata":{"id":"WTbI75qKnNIG"},"source":["# Utility function"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"T3Rx9EwMmx3a"},"outputs":[],"source":["class local_measures_binary:\n"," def __init__(self, G, df):\n"," self.G = G\n"," self.df = df\n"," self.measures = dict()\n"," \n"," self.get_measures()\n"," self.measures = self.get_properties_table()\n","\n"," def get_measures(self):\n"," deg = dict(self.G.degree(self.df))\n"," dc = nx.degree_centrality(self.G)\n"," bc = nx.betweenness_centrality(self.G)\n"," cc = nx.closeness_centrality(self.G)\n"," eig = nx.eigenvector_centrality(self.G)\n"," pgr = nx.pagerank(self.G)\n"," lclu = nx.clustering(self.G)\n"," andeg = nx.average_neighbor_degree(self.G)\n"," lc = nx.load_centrality(self.G)\n"," sc = nx.subgraph_centrality(self.G)\n"," hc = nx.harmonic_centrality(self.G)\n"," lrc = dict()\n"," for i in range(0,164):\n"," lrc[i] = nx.local_reaching_centrality(self.G,i)\n"," ncn = nx.node_clique_number(self.G)\n"," noc = nx.number_of_cliques(self.G)\n"," sqc = nx.square_clustering(self.G)\n"," gcol = nx.greedy_color(self.G)\n","\n"," m = {\n"," 'degree' : deg,\n"," 'degree centrality': dc,\n"," 'betweenness centrality': bc,\n"," 'closeness centrality': cc,\n"," 'eigenvector centrality': eig,\n"," 'pagerank centrality':pgr,\n"," \"local clustering\":lclu,\n"," \"avg neighbour degree\": andeg,\n"," \"load centrality\": lc,\n"," \"subgraph centrality\": sc,\n"," \"harmonic centrality\": hc,\n"," \"local reaching centrality\": lrc,\n"," \"node clique number\": ncn,\n"," \"number of cliques\": noc,\n"," \"square clustering\": sqc,\n"," \"greedy color\": gcol\n"," }\n","\n"," if nx.number_connected_components(self.G) is 1:\n"," soc = nx.second_order_centrality(self.G)\n"," ecc = nx.eccentricity(self.G)\n"," ic = nx.information_centrality(self.G)\n"," cfbc = nx.current_flow_betweenness_centrality(self.G)\n"," acfbc = nx.approximate_current_flow_betweenness_centrality(self.G)\n"," d = {\n"," \"second order clustering\": soc,\n"," \"eccentricity\": ecc,\n"," \"information centrality\": ic,\n"," \"current flow betweenness centrality\": cfbc,\n"," \"approx. current flow betweenness centrality\": acfbc \n"," }\n"," m.update(d)\n","\n"," self.measures.update(m)\n","\n"," def get_properties_table(self):\n"," return pd.DataFrame(self.measures)"]},{"cell_type":"markdown","metadata":{"id":"_6RBG5-rl-8Z"},"source":["# Driver Function"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Gtm0KSzdTFdr"},"outputs":[],"source":["ub = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","dest_dir = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Global features/Newly Generated/'"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true,"base_uri":"https://localhost:8080/"},"id":"6k4yiU7gl-lC","outputId":"40ecda29-b735-44ea-fb2c-e88cede9a1a3"},"outputs":[{"name":"stdout","output_type":"stream","text":["Subject 4018\n","Subject 4021\n","Subject 4023\n","Subject 4014\n","Subject 4016\n","Subject 4019\n","Subject 4024\n","Subject 4022\n","Subject 4025\n","Subject 4009\n","Subject 4017\n","Subject 4000\n","Subject 4001\n","Subject 4006\n","Subject 4015\n","Subject 4005\n","Subject 4002\n","Subject 4003\n","Subject 4013\n","Subject 4008\n","Subject 4010\n","Subject 4007\n","Subject 4020\n","Subject 4004\n","Subject 4011\n","Subject 4012\n","Subject 4041\n","Subject 4043\n","Subject 4061\n","Subject 4066\n","Subject 4034\n","Subject 4032\n","Subject 4051\n","Subject 4069\n","Subject 4067\n","Subject 4029\n","Subject 4035\n","Subject 4037\n","Subject 4028\n","Subject 4039\n","Subject 4062\n","Subject 4060\n","Subject 4038\n","Subject 4058\n","Subject 4047\n","Subject 4055\n","Subject 4072\n","Subject 4075\n","Subject 4050\n","Subject 4048\n","Subject 4074\n","Subject 4042\n","Subject 4068\n","Subject 4026\n","Subject 4073\n","Subject 4057\n","Subject 4054\n","Subject 4064\n","Subject 4052\n","Subject 4033\n","Subject 4030\n","Subject 4045\n","Subject 4071\n","Subject 4040\n","Subject 4056\n","Subject 4065\n","Subject 4063\n","Subject 4053\n","Subject 4031\n","Subject 4070\n","Subject 4036\n","Subject 4059\n","Subject 4027\n","Subject 4049\n","Subject 4044\n","Subject 4046\n","Subject 4098\n","Subject 4113\n","Subject 4103\n","Subject 4107\n","Subject 4077\n","Subject 4120\n","Subject 4100\n","Subject 4109\n","Subject 4080\n","Subject 4086\n","Subject 4091\n","Subject 4078\n","Subject 4079\n","Subject 4093\n","Subject 4112\n","Subject 4111\n","Subject 4090\n","Subject 4089\n","Subject 4104\n","Subject 4101\n","Subject 4108\n","Subject 4087\n","Subject 4083\n","Subject 4097\n","Subject 4123\n","Subject 4118\n","Subject 4117\n","Subject 4114\n","Subject 4124\n","Subject 4085\n","Subject 4099\n","Subject 4102\n","Subject 4116\n","Subject 4084\n","Subject 4119\n","Subject 4096\n","Subject 4088\n","Subject 4106\n","Subject 4105\n","Subject 4121\n","Subject 4094\n","Subject 4125\n","Subject 4092\n","Subject 4082\n","Subject 4110\n","Subject 4081\n","Subject 4115\n","Subject 4122\n","Subject 4095\n","Subject 4147\n","Subject 4076\n","Subject 4169\n","Subject 4129\n","Subject 4128\n","Subject 4144\n","Subject 4150\n","Subject 4141\n","Subject 4142\n","Subject 4154\n","Subject 4165\n","Subject 4143\n","Subject 4146\n","Subject 4151\n","Subject 4137\n","Subject 4161\n","Subject 4156\n","Subject 4157\n","Subject 4133\n","Subject 4135\n","Subject 4167\n","Subject 4136\n","Subject 4168\n","Subject 4164\n","Subject 4127\n","Subject 4170\n","Subject 4148\n","Subject 4171\n","Subject 4166\n","Subject 4153\n","Subject 4158\n","Subject 4159\n","Subject 4139\n","Subject 4162\n","Subject 4145\n","Subject 4163\n","Subject 4149\n","Subject 4140\n","Subject 4130\n","Subject 4134\n","Subject 4126\n","Subject 4131\n","Subject 4160\n","Subject 4155\n","Subject 4138\n","Subject 4152\n","Subject 4132\n"]}],"source":["# Add the directories as per requirement\n","dirs = [ub] \n","for dir in dirs:\n"," for file in os.listdir(dir):\n"," if file.endswith(\".csv\"):\n"," if (dir == ub):\n"," subject = file[12:16]\n"," elif (dir == uw):\n"," subject = file[14:18]\n"," else:\n"," print(\"If you are using a statically binarized folder:\")\n"," print(\"Add a condition along with cb condition for COBRE and ub condition for UCLA\")\n"," print(\"Example: elif (dir == ub) becomes elif (dir == ub) or (dir == ub0_3)\")\n"," exit(0)\n","\n"," # APPENDING CORRESPONDING GRAPH - may change based on implementation\n"," df = pd.read_csv(dir+file, header=None)\n"," G = nx.from_pandas_adjacency(df)\n"," res = local_measures_binary(G, df)\n"," \n"," res.measures.to_csv(dest_dir+'binary_node_features_'+file)\n"," print(\"Subject\",subject)"]},{"cell_type":"markdown","metadata":{"id":"wPPy9VNMoaCu"},"source":["# Results"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true},"id":"qoUAOiO7jtnQ","outputId":"376cf7c6-1dc3-4528-cabd-960689b4b103"},"outputs":[{"data":{"text/html":["\n","
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degreedegree centralitybetweenness centralitycloseness centralityeigenvector centralitypagerank centralitylocal clusteringavg neighbour degreeload centralitysubgraph centrality...local reaching centralitynode clique numbernumber of cliquessquare clusteringgreedy colorsecond order clusteringeccentricityinformation centralitycurrent flow betweenness centralityapprox. current flow betweenness centrality
0580.3558280.0033690.5927270.1035920.0068210.62552956.4827590.0033904.327763e+21...0.670757248660.36990822216.16174230.1529210.0150400.015826
1620.3803680.0034490.6150940.1119470.0071880.61078857.2580650.0033975.054098e+21...0.689162258460.3657156204.79149930.1574250.0154880.015796
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3580.3558280.0051740.5927270.0961820.0068870.54507055.1034480.0051603.730728e+21...0.670757244040.31012910215.40705630.1532190.0171960.018117
4340.2085890.0014230.5415280.0375000.0046050.62210345.8529410.0014875.670813e+20...0.59509215820.30460020315.05119430.1163790.0114460.011162
..................................................................
159450.2760740.0037540.5699300.0474030.0058480.55252546.6444440.0037909.060653e+20...0.632924163060.28667017261.43132930.1354210.0152510.016816
160440.2699390.0023510.5699300.0438100.0057530.59936646.7500000.0023747.738830e+20...0.630879173070.30453718265.88336030.1337580.0144650.017282
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164 rows × 21 columns

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\n"," \n"," \n"," \n","\n"," \n","
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\n"," "],"text/plain":[" degree degree centrality betweenness centrality closeness centrality \\\n","0 58 0.355828 0.003369 0.592727 \n","1 62 0.380368 0.003449 0.615094 \n","2 63 0.386503 0.003039 0.612782 \n","3 58 0.355828 0.005174 0.592727 \n","4 34 0.208589 0.001423 0.541528 \n",".. ... ... ... ... \n","159 45 0.276074 0.003754 0.569930 \n","160 44 0.269939 0.002351 0.569930 \n","161 45 0.276074 0.004404 0.562069 \n","162 48 0.294479 0.004050 0.584229 \n","163 56 0.343558 0.004376 0.599265 \n","\n"," eigenvector centrality pagerank centrality local clustering \\\n","0 0.103592 0.006821 0.625529 \n","1 0.111947 0.007188 0.610788 \n","2 0.116265 0.007271 0.638505 \n","3 0.096182 0.006887 0.545070 \n","4 0.037500 0.004605 0.622103 \n",".. ... ... ... \n","159 0.047403 0.005848 0.552525 \n","160 0.043810 0.005753 0.599366 \n","161 0.040425 0.005958 0.533333 \n","162 0.075903 0.005894 0.520390 \n","163 0.097633 0.006623 0.572078 \n","\n"," avg neighbour degree load centrality subgraph centrality ... \\\n","0 56.482759 0.003390 4.327763e+21 ... \n","1 57.258065 0.003397 5.054098e+21 ... \n","2 58.476190 0.003034 5.451467e+21 ... \n","3 55.103448 0.005160 3.730728e+21 ... \n","4 45.852941 0.001487 5.670813e+20 ... \n",".. ... ... ... ... \n","159 46.644444 0.003790 9.060653e+20 ... \n","160 46.750000 0.002374 7.738830e+20 ... \n","161 43.066667 0.004448 6.589125e+20 ... \n","162 55.291667 0.004062 2.323333e+21 ... \n","163 57.339286 0.004402 3.844134e+21 ... \n","\n"," local reaching centrality node clique number number of cliques \\\n","0 0.670757 24 866 \n","1 0.689162 25 846 \n","2 0.690184 26 1236 \n","3 0.670757 24 404 \n","4 0.595092 15 82 \n",".. ... ... ... \n","159 0.632924 16 306 \n","160 0.630879 17 307 \n","161 0.628834 16 243 \n","162 0.646217 16 302 \n","163 0.669734 24 437 \n","\n"," square clustering greedy color second order clustering eccentricity \\\n","0 0.369908 22 216.161742 3 \n","1 0.365715 6 204.791499 3 \n","2 0.375446 19 202.142903 3 \n","3 0.310129 10 215.407056 3 \n","4 0.304600 20 315.051194 3 \n",".. ... ... ... ... \n","159 0.286670 17 261.431329 3 \n","160 0.304537 18 265.883360 3 \n","161 0.286043 9 262.207867 3 \n","162 0.273896 6 247.896667 3 \n","163 0.327503 24 221.365223 3 \n","\n"," information centrality current flow betweenness centrality \\\n","0 0.152921 0.015040 \n","1 0.157425 0.015488 \n","2 0.158476 0.015348 \n","3 0.153219 0.017196 \n","4 0.116379 0.011446 \n",".. ... ... \n","159 0.135421 0.015251 \n","160 0.133758 0.014465 \n","161 0.135130 0.016256 \n","162 0.140549 0.015432 \n","163 0.150868 0.015646 \n","\n"," approx. current flow betweenness centrality \n","0 0.015826 \n","1 0.015796 \n","2 0.016063 \n","3 0.018117 \n","4 0.011162 \n",".. ... \n","159 0.016816 \n","160 0.017282 \n","161 0.020894 \n","162 0.016149 \n","163 0.019778 \n","\n","[164 rows x 21 columns]"]},"execution_count":12,"metadata":{},"output_type":"execute_result"}],"source":["res.measures"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/1. Feature Generation/Local Weighted Measures.ipynb b/Code/1. Feature Generation/Local Weighted Measures.ipynb new file mode 100644 index 0000000..03827a3 --- /dev/null +++ b/Code/1. Feature Generation/Local Weighted Measures.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"id":"b6465562-8ef4-4cce-b589-4bf396b72d88","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.681431Z","start_time":"2022-09-01T14:16:18.996297Z"},"id":"b6465562-8ef4-4cce-b589-4bf396b72d88","outputId":"f51bb94a-fd6a-4327-c450-cfb1dccd18ef"},"outputs":[{"name":"stdout","output_type":"stream","text":["Metal device set to: Apple M1 Pro\n"]},{"name":"stderr","output_type":"stream","text":["2022-09-29 16:40:43.892988: I tensorflow/core/common_runtime/pluggable_device/pluggable_device_factory.cc:305] Could not identify NUMA node of platform GPU ID 0, defaulting to 0. Your kernel may not have been built with NUMA support.\n","2022-09-29 16:40:43.893315: I tensorflow/core/common_runtime/pluggable_device/pluggable_device_factory.cc:271] Created TensorFlow device (/job:localhost/replica:0/task:0/device:GPU:0 with 0 MB memory) -> physical PluggableDevice (device: 0, name: METAL, pci bus id: )\n"]}],"source":["#imports \n","\n","from stellargraph import StellarGraph\n","import stellargraph as sg\n","from stellargraph.mapper import PaddedGraphGenerator\n","from stellargraph.layer import DeepGraphCNN\n","import pandas as pd\n","import os\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","\n","from sklearn import model_selection\n","from IPython.display import display, HTML\n","\n","from tensorflow.keras import Model\n","from tensorflow.keras.optimizers import Adam\n","from tensorflow.keras.layers import Dense, Conv1D, MaxPool1D, Dropout, Flatten\n","from tensorflow.keras.losses import binary_crossentropy\n","import tensorflow as tf\n","from tensorflow import keras"]},{"cell_type":"code","execution_count":null,"id":"35043e60-8ee2-466a-b238-0155bd5ed901","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.691586Z","start_time":"2022-09-01T14:16:20.682684Z"},"id":"35043e60-8ee2-466a-b238-0155bd5ed901","outputId":"64523b08-d833-4810-f7a7-f41d4742d925"},"outputs":[{"data":{"text/html":["
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SubjectSubject TypeLabel
040013Control0
140014Control0
240017Control0
340018Control0
440019Control0
............
4162168Patient1
4172169Patient1
4182170Patient1
4192171Patient1
4202172Patient1
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421 rows × 3 columns

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"],"text/plain":[" Subject Subject Type Label\n","0 40013 Control 0\n","1 40014 Control 0\n","2 40017 Control 0\n","3 40018 Control 0\n","4 40019 Control 0\n",".. ... ... ...\n","416 2168 Patient 1\n","417 2169 Patient 1\n","418 2170 Patient 1\n","419 2171 Patient 1\n","420 2172 Patient 1\n","\n","[421 rows x 3 columns]"]},"execution_count":2,"metadata":{},"output_type":"execute_result"}],"source":["combined_phenotype = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","labels_mappings"]},{"cell_type":"code","execution_count":null,"id":"41482575-e663-4a45-bb6a-89a1bb957e8c","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.694814Z","start_time":"2022-09-01T14:16:20.692476Z"},"id":"41482575-e663-4a45-bb6a-89a1bb957e8c"},"outputs":[],"source":["def row_transform(arr, threshold):\n"," for i in range(len(arr)):\n"," arr[i] = arr[i] if arr[i]> threshold else abs(arr[i])+0.0001\n"," return arr\n","\n","def binarize(df, threshold):\n"," df = df.transform(lambda x: row_transform(x, threshold))"]},{"cell_type":"code","execution_count":null,"id":"64ad9c6b-103c-4c08-a601-8c676fead8a9","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.698854Z","start_time":"2022-09-01T14:16:20.697197Z"},"id":"64ad9c6b-103c-4c08-a601-8c676fead8a9"},"outputs":[],"source":["uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'"]},{"cell_type":"code","execution_count":null,"id":"05fff533","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.701227Z","start_time":"2022-09-01T14:16:20.699595Z"},"id":"05fff533"},"outputs":[],"source":["dirs=[uw]\n","count = 0 "]},{"cell_type":"code","execution_count":null,"id":"1a9bd4a7","metadata":{"ExecuteTime":{"end_time":"2022-09-01T14:16:20.703445Z","start_time":"2022-09-01T14:16:20.701965Z"},"id":"1a9bd4a7"},"outputs":[],"source":["graphs = list()\n","graph_labels = list()\n","sub_lst = list(range(0,164))"]},{"cell_type":"code","execution_count":null,"id":"8e19c8b2-515c-4199-b03c-78b846699ee1","metadata":{"ExecuteTime":{"end_time":"2022-09-04T12:28:03.198174Z","start_time":"2022-09-01T14:16:20.704592Z"},"id":"8e19c8b2-515c-4199-b03c-78b846699ee1","outputId":"6ada93f3-345b-4cfa-9e8f-6a66703244b1"},"outputs":[{"name":"stdout","output_type":"stream","text":["1\n","2\n","3\n","4\n","5\n","6\n","7\n","8\n","9\n","10\n","11\n","12\n","13\n","14\n","15\n","16\n","17\n","18\n","19\n","20\n","21\n"]}],"source":["for dir in dirs:\n"," for file in os.listdir(dir):\n"," if file.endswith(\".csv\"):\n"," subject = file[14:18]\n"," df = pd.read_csv(dir+'/'+file, header=None)\n"," binarize(df,0)\n"," df = df.replace(np.nan ,0)\n"," G = nx.from_pandas_adjacency(df)\n","\n"," #adding other attributes\n"," wd = dict(G.degree(weight='weight'))\n"," cv = nx.closeness_vitality(G, node=None, weight=\"weight\", wiener_index=None)\n"," andeg = nx.average_neighbor_degree(G, weight=\"weight\")\n"," cons = nx.constraint(G, nodes=None, weight=\"weight\")\n"," es = nx.effective_size(G, nodes=None, weight=\"weight\")\n"," \n"," node_features_data=list(zip(wd.values(),cv.values(),andeg.values(),cons.values(),es.values()))\n"," node_features_columns= ['weighted degree','closeness vitality','avg neighbor degree',\n"," 'constraint','effective size']\n"," node_data= pd.DataFrame(node_features_data, index=sub_lst, columns=node_features_columns)\n"," \n"," #saving individual node features\n"," csv_path='weighted_node_features_'+str(subject)+'.csv'\n"," node_data.to_csv(csv_path)\n"," \n"," count+=1\n"," print(count)"]}],"metadata":{"kernelspec":{"display_name":"Python 3 (ipykernel)","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.10.6"},"toc":{"base_numbering":1,"nav_menu":{},"number_sections":true,"sideBar":true,"skip_h1_title":false,"title_cell":"Table of Contents","title_sidebar":"Contents","toc_cell":false,"toc_position":{},"toc_section_display":true,"toc_window_display":false},"colab":{"provenance":[]}},"nbformat":4,"nbformat_minor":5} \ No newline at end of file diff --git a/Code/2. Threshold Comparison/XGB for threshold comparison.ipynb b/Code/2. Threshold Comparison/XGB for threshold comparison.ipynb new file mode 100644 index 0000000..2f37c43 --- /dev/null +++ b/Code/2. Threshold Comparison/XGB for threshold comparison.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# IMPORT"],"metadata":{"id":"Ipf2gJ0dRMjb"}},{"cell_type":"code","execution_count":null,"metadata":{"id":"9R8R0jALQ_7H"},"outputs":[],"source":["import pandas as pd \n","import numpy as np\n","import statistics\n","from sklearn import preprocessing,svm\n","from sklearn.metrics import *\n","from sklearn.neighbors import KNeighborsRegressor\n","from sklearn.preprocessing import StandardScaler, Normalizer, MinMaxScaler\n","from itertools import product, combinations\n","from sklearn.ensemble import AdaBoostClassifier\n","from xgboost import XGBClassifier\n","from sklearn.model_selection import GridSearchCV, cross_val_score, StratifiedKFold, train_test_split, LeaveOneOut, RepeatedStratifiedKFold, RandomizedSearchCV\n","import itertools\n","import matplotlib.pyplot as plt\n","from sklearn.pipeline import Pipeline\n","import cvxopt\n","import matplotlib.mlab as mlab\n","import seaborn\n","import pickle\n","\n","\n","%matplotlib inline"]},{"cell_type":"markdown","source":["# DATA LOADING"],"metadata":{"id":"FO2_ByN3Rp7E"}},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nQOVc2CdRpNd","outputId":"d6a00675-227a-4197-c43d-c12d34d4b443","executionInfo":{"status":"ok","timestamp":1671425508786,"user_tz":-330,"elapsed":37088,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}]},{"cell_type":"code","source":["df0_path = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Binary features for all thresholds/global_binary_ucla_0_0.csv'\n","df1_path = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Binary features for all thresholds/global_binary_ucla_0_1.csv'\n","df2_path = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Binary features for all thresholds/global_binary_ucla_0_2.csv'\n","df3_path = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Binary features for all thresholds/global_binary_ucla_0_3.csv'"],"metadata":{"id":"m6T6JlieZduW"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Check: [this link](https://https://drive.google.com/drive/folders/1Qt7MZEBx--dPemipKRfioL-6f7cjZeAt?usp=share_link) for all thresholds to get the names of other thresholds "],"metadata":{"id":"HWOcYDyNulk8"}},{"cell_type":"code","source":["df0 = pd.read_csv(df0_path)\n","df0.drop(['Unnamed: 0'], axis = 1, inplace = True, errors='ignore')\n","df0s"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":922},"id":"b5COjwRfaV2U","outputId":"0eef32e1-0189-4b6f-9695-66e1d0f18fd6"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Schizophrenic Approximation and Heuristics Node Connectivity \\\n","0 2019.0 0.0 43.0 \n","1 2024.0 0.0 62.0 \n","2 2022.0 0.0 42.0 \n","3 2015.0 0.0 60.0 \n","4 2025.0 0.0 50.0 \n",".. ... ... ... \n","167 2162.0 1.0 52.0 \n","168 2157.0 1.0 59.0 \n","169 2139.0 1.0 47.0 \n","170 2133.0 1.0 57.0 \n","171 2153.0 1.0 60.0 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","0 {128, 0, 4, 147, 89, 156} \n","1 {33, 4, 134, 8, 12, 56} \n","2 {1, 100, 5, 36, 159} \n","3 {128, 0, 76, 148, 29} \n","4 {130, 100, 5, 6, 9, 154} \n",".. ... \n","167 {131, 36, 5, 7, 142, 28} \n","168 {0, 1, 163, 16, 124} \n","169 {128, 161, 135, 39, 9, 56} \n","170 {100, 18, 122, 156, 30} \n","171 {136, 8, 108, 143, 154} \n","\n"," Approximation and Heuristics Max Cliques \\\n","0 {11, 13, 14, 15, 16, 17, 21, 22, 23, 26, 27, 2... \n","1 {5, 6, 7, 10, 145, 44, 45, 46, 47, 48, 51, 52,... \n","2 {0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 32... \n","3 {6, 7, 8, 9, 10, 145, 146, 147, 21, 150, 157, ... \n","4 {129, 8, 141, 19, 22, 23, 28, 29, 31, 32, 33, ... \n",".. ... \n","167 {20, 21, 151, 162, 46, 48, 52, 53, 58, 67, 76,... \n","168 {5, 135, 136, 9, 138, 139, 140, 141, 7, 146, 1... \n","169 {4, 5, 6, 7, 144, 17, 16, 147, 20, 21, 151, 15... \n","170 {0, 129, 130, 3, 2, 1, 8, 15, 22, 23, 24, 25, ... \n","171 {0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, 3... \n","\n"," Approximation and Heuristics Clique Removal \\\n","0 ({128, 0, 4, 147, 89, 156}, [{4, 133, 6, 5, 16... \n","1 ({33, 4, 134, 8, 12, 56}, [{0, 1, 2, 131, 3, 6... \n","2 ({1, 100, 5, 36, 159}, [{0, 1, 2, 131, 4, 133,... \n","3 ({128, 0, 76, 148, 29}, [{128, 129, 134, 12, 1... \n","4 ({130, 100, 5, 6, 9, 154}, [{0, 1, 2, 3, 4, 14... \n",".. ... \n","167 ({131, 36, 5, 7, 142, 28}, [{13, 17, 146, 148,... \n","168 ({0, 1, 163, 16, 124}, [{160, 161, 162, 3, 1, ... \n","169 ({128, 161, 135, 39, 9, 56}, [{4, 5, 6, 7, 144... \n","170 ({100, 18, 122, 156, 30}, [{0, 129, 130, 3, 2,... \n","171 ({136, 8, 108, 143, 154}, [{0, 1, 130, 3, 2, 1... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 39.0 \n","1 31.0 \n","2 32.0 \n","3 30.0 \n","4 26.0 \n",".. ... \n","167 25.0 \n","168 29.0 \n","169 36.0 \n","170 37.0 \n","171 40.0 \n","\n"," Approximation and Heuristics Average Clustering \\\n","0 0.674 \n","1 0.613 \n","2 0.658 \n","3 0.661 \n","4 0.647 \n",".. ... \n","167 0.634 \n","168 0.678 \n","169 0.683 \n","170 0.697 \n","171 0.734 \n","\n"," Approximation and Heuristics Diameter \\\n","0 2.0 \n","1 2.0 \n","2 2.0 \n","3 2.0 \n","4 2.0 \n",".. ... \n","167 2.0 \n","168 2.0 \n","169 2.0 \n","170 2.0 \n","171 2.0 \n","\n"," Approximation and Heuristics Min Edge Dominating Set ... Chordal \\\n","0 {(54, 55), (100, 101), (40, 41), (72, 73), (18... ... False \n","1 {(54, 55), (86, 87), (100, 101), (154, 156), (... ... False \n","2 {(54, 55), (86, 87), (154, 156), (40, 41), (72... ... False \n","3 {(54, 55), (86, 87), (100, 101), (125, 126), (... ... False \n","4 {(54, 55), (86, 87), (92, 93), (156, 157), (40... ... False \n",".. ... ... ... \n","167 {(6, 9), (54, 55), (86, 87), (10, 17), (100, 1... ... False \n","168 {(54, 55), (86, 87), (92, 93), (100, 101), (40... ... False \n","169 {(54, 55), (86, 87), (92, 93), (100, 101), (15... ... False \n","170 {(86, 87), (100, 101), (156, 157), (40, 41), (... ... False \n","171 {(54, 55), (92, 93), (156, 157), (40, 41), (72... ... False \n","\n"," Maximal Cliques Num of isolates Non Randomness wrt Random Model \\\n","0 227045.0 0.0 7.277249 \n","1 165809.0 0.0 2.495979 \n","2 261112.0 0.0 3.893600 \n","3 33730.0 0.0 0.766125 \n","4 289857.0 0.0 2.706520 \n",".. ... ... ... \n","167 229522.0 0.0 2.672876 \n","168 178971.0 0.0 1.901956 \n","169 481345.0 0.0 5.175136 \n","170 169682.0 0.0 3.187179 \n","171 592404.0 0.0 3.848097 \n","\n"," Transitivity Connected Components Diameter 1 Edge Connected \\\n","0 0.698336 1.0 2.0 True \n","1 0.644565 1.0 2.0 True \n","2 0.666596 1.0 2.0 True \n","3 0.652857 1.0 2.0 True \n","4 0.640787 1.0 2.0 True \n",".. ... ... ... ... \n","167 0.634603 1.0 2.0 True \n","168 0.652782 1.0 2.0 True \n","169 0.701991 1.0 2.0 True \n","170 0.668056 1.0 2.0 True \n","171 0.717857 1.0 2.0 True \n","\n"," 2 Edge Connected 3 Edge Connected \n","0 True True \n","1 True True \n","2 True True \n","3 True True \n","4 True True \n",".. ... ... \n","167 True True \n","168 True True \n","169 True True \n","170 True True \n","171 True True \n","\n","[172 rows x 38 columns]"],"text/html":["\n","
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SubjectSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating Set...ChordalMaximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge Connected
02019.00.043.0{128, 0, 4, 147, 89, 156}{11, 13, 14, 15, 16, 17, 21, 22, 23, 26, 27, 2...({128, 0, 4, 147, 89, 156}, [{4, 133, 6, 5, 16...39.00.6742.0{(54, 55), (100, 101), (40, 41), (72, 73), (18......False227045.00.07.2772490.6983361.02.0TrueTrueTrue
12024.00.062.0{33, 4, 134, 8, 12, 56}{5, 6, 7, 10, 145, 44, 45, 46, 47, 48, 51, 52,...({33, 4, 134, 8, 12, 56}, [{0, 1, 2, 131, 3, 6...31.00.6132.0{(54, 55), (86, 87), (100, 101), (154, 156), (......False165809.00.02.4959790.6445651.02.0TrueTrueTrue
22022.00.042.0{1, 100, 5, 36, 159}{0, 1, 2, 131, 4, 133, 3, 135, 140, 24, 30, 32...({1, 100, 5, 36, 159}, [{0, 1, 2, 131, 4, 133,...32.00.6582.0{(54, 55), (86, 87), (154, 156), (40, 41), (72......False261112.00.03.8936000.6665961.02.0TrueTrueTrue
32015.00.060.0{128, 0, 76, 148, 29}{6, 7, 8, 9, 10, 145, 146, 147, 21, 150, 157, ...({128, 0, 76, 148, 29}, [{128, 129, 134, 12, 1...30.00.6612.0{(54, 55), (86, 87), (100, 101), (125, 126), (......False33730.00.00.7661250.6528571.02.0TrueTrueTrue
42025.00.050.0{130, 100, 5, 6, 9, 154}{129, 8, 141, 19, 22, 23, 28, 29, 31, 32, 33, ...({130, 100, 5, 6, 9, 154}, [{0, 1, 2, 3, 4, 14...26.00.6472.0{(54, 55), (86, 87), (92, 93), (156, 157), (40......False289857.00.02.7065200.6407871.02.0TrueTrueTrue
..................................................................
1672162.01.052.0{131, 36, 5, 7, 142, 28}{20, 21, 151, 162, 46, 48, 52, 53, 58, 67, 76,...({131, 36, 5, 7, 142, 28}, [{13, 17, 146, 148,...25.00.6342.0{(6, 9), (54, 55), (86, 87), (10, 17), (100, 1......False229522.00.02.6728760.6346031.02.0TrueTrueTrue
1682157.01.059.0{0, 1, 163, 16, 124}{5, 135, 136, 9, 138, 139, 140, 141, 7, 146, 1...({0, 1, 163, 16, 124}, [{160, 161, 162, 3, 1, ...29.00.6782.0{(54, 55), (86, 87), (92, 93), (100, 101), (40......False178971.00.01.9019560.6527821.02.0TrueTrueTrue
1692139.01.047.0{128, 161, 135, 39, 9, 56}{4, 5, 6, 7, 144, 17, 16, 147, 20, 21, 151, 15...({128, 161, 135, 39, 9, 56}, [{4, 5, 6, 7, 144...36.00.6832.0{(54, 55), (86, 87), (92, 93), (100, 101), (15......False481345.00.05.1751360.7019911.02.0TrueTrueTrue
1702133.01.057.0{100, 18, 122, 156, 30}{0, 129, 130, 3, 2, 1, 8, 15, 22, 23, 24, 25, ...({100, 18, 122, 156, 30}, [{0, 129, 130, 3, 2,...37.00.6972.0{(86, 87), (100, 101), (156, 157), (40, 41), (......False169682.00.03.1871790.6680561.02.0TrueTrueTrue
1712153.01.060.0{136, 8, 108, 143, 154}{0, 1, 130, 3, 2, 139, 140, 141, 26, 27, 28, 3...({136, 8, 108, 143, 154}, [{0, 1, 130, 3, 2, 1...40.00.7342.0{(54, 55), (92, 93), (156, 157), (40, 41), (72......False592404.00.03.8480970.7178571.02.0TrueTrueTrue
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172 rows × 38 columns

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\n"," "]},"metadata":{},"execution_count":23}]},{"cell_type":"code","source":["df1 = pd.read_csv(df1_path)\n","df1.drop(['Unnamed: 0'], axis = 1, inplace = True, errors='ignore')\n","df1"],"metadata":{"id":"L_iwO_g2ag0d","colab":{"base_uri":"https://localhost:8080/","height":939},"outputId":"b5fbef63-574f-4858-9a78-c4ac427b080c"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Schizophrenic Approximation and Heuristics Node Connectivity \\\n","0 2024.0 0.0 29.0 \n","1 2019.0 0.0 27.0 \n","2 2022.0 0.0 28.0 \n","3 2015.0 0.0 34.0 \n","4 2025.0 0.0 28.0 \n",".. ... ... ... \n","167 2162.0 1.0 28.0 \n","168 2157.0 1.0 31.0 \n","169 2139.0 1.0 21.0 \n","170 2133.0 1.0 35.0 \n","171 2153.0 1.0 32.0 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","0 {121, 107, 11, 48, 18, 20, 22, 153, 154} \n","1 {3, 11, 48, 18, 116, 153, 154, 124} \n","2 {128, 26, 10, 50, 86, 23, 58, 156} \n","3 {0, 129, 4, 9, 107, 52, 152} \n","4 {128, 34, 4, 134, 135, 104, 7, 55, 25} \n",".. ... \n","167 {160, 11, 44, 141, 80, 18, 156, 62, 127} \n","168 {36, 69, 11, 155, 13, 15, 19, 59, 157} \n","169 {128, 0, 132, 4, 72, 153, 126} \n","170 {130, 138, 109, 114, 21, 150, 25, 126} \n","171 {128, 135, 137, 143, 16, 49, 50, 22} \n","\n"," Approximation and Heuristics Max Cliques \\\n","0 {160, 97, 66, 8, 41, 138, 106, 74, 42, 78, 10,... \n","1 {13, 14, 15, 16, 17, 21, 23, 27, 28, 35, 36, 3... \n","2 {12, 13, 15, 16, 17, 19, 148, 21, 150, 20, 34,... \n","3 {5, 6, 8, 10, 145, 146, 147, 19, 21, 150, 159,... \n","4 {32, 33, 130, 129, 3, 37, 2, 39, 72, 73, 1, 75... \n",".. ... \n","167 {69, 38, 71, 40, 41, 42, 39, 13, 16, 17, 19, 2... \n","168 {7, 8, 9, 138, 139, 140, 10, 146, 147, 148, 14... \n","169 {11, 12, 13, 14, 15, 16, 17, 28, 29, 34, 35, 4... \n","170 {0, 1, 2, 3, 8, 23, 24, 28, 29, 32, 33, 38, 54... \n","171 {0, 1, 130, 3, 2, 139, 30, 31, 36, 37, 39, 46,... \n","\n"," Approximation and Heuristics Clique Removal \\\n","0 ({121, 107, 11, 48, 18, 20, 22, 153, 154}, [{3... \n","1 ({3, 11, 48, 18, 116, 153, 154, 124}, [{4, 101... \n","2 ({128, 26, 10, 50, 86, 23, 58, 156}, [{0, 1, 2... \n","3 ({0, 129, 4, 9, 107, 52, 152}, [{128, 130, 35,... \n","4 ({128, 34, 4, 134, 135, 104, 7, 55, 25}, [{32,... \n",".. ... \n","167 ({160, 11, 44, 141, 80, 18, 156, 62, 127}, [{6... \n","168 ({36, 69, 11, 155, 13, 15, 19, 59, 157}, [{1, ... \n","169 ({128, 0, 132, 4, 72, 153, 126}, [{4, 5, 6, 7,... \n","170 ({130, 138, 109, 114, 21, 150, 25, 126}, [{0, ... \n","171 ({128, 135, 137, 143, 16, 49, 50, 22}, [{0, 1,... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 24.0 \n","1 30.0 \n","2 22.0 \n","3 26.0 \n","4 20.0 \n",".. ... \n","167 20.0 \n","168 23.0 \n","169 30.0 \n","170 30.0 \n","171 31.0 \n","\n"," Approximation and Heuristics Average Clustering \\\n","0 0.566 \n","1 0.622 \n","2 0.612 \n","3 0.602 \n","4 0.533 \n",".. ... \n","167 0.523 \n","168 0.554 \n","169 0.627 \n","170 0.598 \n","171 0.628 \n","\n"," Approximation and Heuristics Diameter \\\n","0 3.0 \n","1 3.0 \n","2 2.0 \n","3 3.0 \n","4 2.0 \n",".. ... \n","167 2.0 \n","168 2.0 \n","169 2.0 \n","170 2.0 \n","171 2.0 \n","\n"," Approximation and Heuristics Min Edge Dominating Set ... Chordal \\\n","0 {(54, 55), (86, 87), (100, 101), (154, 156), (... ... False \n","1 {(54, 55), (100, 101), (125, 126), (40, 41), (... ... False \n","2 {(54, 55), (86, 87), (154, 156), (72, 73), (18... ... False \n","3 {(54, 55), (86, 87), (125, 126), (40, 41), (72... ... False \n","4 {(54, 55), (86, 87), (92, 93), (125, 126), (30... ... False \n",".. ... ... ... \n","167 {(6, 9), (54, 55), (86, 87), (40, 41), (72, 73... ... False \n","168 {(86, 87), (92, 93), (100, 101), (125, 126), (... ... False \n","169 {(54, 55), (86, 87), (100, 101), (125, 126), (... ... False \n","170 {(86, 87), (125, 126), (156, 157), (40, 41), (... ... False \n","171 {(54, 55), (86, 87), (92, 93), (156, 157), (40... ... False \n","\n"," Maximal Cliques Num of isolates Non Randomness wrt Random Model \\\n","0 17184.0 0.0 4.553827 \n","1 28416.0 0.0 10.303074 \n","2 26690.0 0.0 5.002479 \n","3 7333.0 0.0 1.096650 \n","4 20187.0 0.0 4.359957 \n",".. ... ... ... \n","167 17203.0 0.0 3.144129 \n","168 25882.0 0.0 -24.921649 \n","169 45641.0 0.0 6.708431 \n","170 24061.0 0.0 4.809681 \n","171 62094.0 0.0 6.214514 \n","\n"," Transitivity Connected Components Diameter 1 Edge Connected \\\n","0 0.555932 1.0 3.0 True \n","1 0.635582 1.0 3.0 True \n","2 0.580028 1.0 3.0 True \n","3 0.608700 1.0 3.0 True \n","4 0.539438 1.0 3.0 True \n",".. ... ... ... ... \n","167 0.539863 1.0 3.0 True \n","168 0.569801 1.0 3.0 True \n","169 0.625999 1.0 3.0 True \n","170 0.598039 1.0 3.0 True \n","171 0.626438 1.0 3.0 True \n","\n"," 2 Edge Connected 3 Edge Connected \n","0 True True \n","1 True True \n","2 True True \n","3 True True \n","4 True True \n",".. ... ... \n","167 True True \n","168 True True \n","169 True True \n","170 True True \n","171 True True \n","\n","[172 rows x 38 columns]"],"text/html":["\n","
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SubjectSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating Set...ChordalMaximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge Connected
02024.00.029.0{121, 107, 11, 48, 18, 20, 22, 153, 154}{160, 97, 66, 8, 41, 138, 106, 74, 42, 78, 10,...({121, 107, 11, 48, 18, 20, 22, 153, 154}, [{3...24.00.5663.0{(54, 55), (86, 87), (100, 101), (154, 156), (......False17184.00.04.5538270.5559321.03.0TrueTrueTrue
12019.00.027.0{3, 11, 48, 18, 116, 153, 154, 124}{13, 14, 15, 16, 17, 21, 23, 27, 28, 35, 36, 3...({3, 11, 48, 18, 116, 153, 154, 124}, [{4, 101...30.00.6223.0{(54, 55), (100, 101), (125, 126), (40, 41), (......False28416.00.010.3030740.6355821.03.0TrueTrueTrue
22022.00.028.0{128, 26, 10, 50, 86, 23, 58, 156}{12, 13, 15, 16, 17, 19, 148, 21, 150, 20, 34,...({128, 26, 10, 50, 86, 23, 58, 156}, [{0, 1, 2...22.00.6122.0{(54, 55), (86, 87), (154, 156), (72, 73), (18......False26690.00.05.0024790.5800281.03.0TrueTrueTrue
32015.00.034.0{0, 129, 4, 9, 107, 52, 152}{5, 6, 8, 10, 145, 146, 147, 19, 21, 150, 159,...({0, 129, 4, 9, 107, 52, 152}, [{128, 130, 35,...26.00.6023.0{(54, 55), (86, 87), (125, 126), (40, 41), (72......False7333.00.01.0966500.6087001.03.0TrueTrueTrue
42025.00.028.0{128, 34, 4, 134, 135, 104, 7, 55, 25}{32, 33, 130, 129, 3, 37, 2, 39, 72, 73, 1, 75...({128, 34, 4, 134, 135, 104, 7, 55, 25}, [{32,...20.00.5332.0{(54, 55), (86, 87), (92, 93), (125, 126), (30......False20187.00.04.3599570.5394381.03.0TrueTrueTrue
..................................................................
1672162.01.028.0{160, 11, 44, 141, 80, 18, 156, 62, 127}{69, 38, 71, 40, 41, 42, 39, 13, 16, 17, 19, 2...({160, 11, 44, 141, 80, 18, 156, 62, 127}, [{6...20.00.5232.0{(6, 9), (54, 55), (86, 87), (40, 41), (72, 73......False17203.00.03.1441290.5398631.03.0TrueTrueTrue
1682157.01.031.0{36, 69, 11, 155, 13, 15, 19, 59, 157}{7, 8, 9, 138, 139, 140, 10, 146, 147, 148, 14...({36, 69, 11, 155, 13, 15, 19, 59, 157}, [{1, ...23.00.5542.0{(86, 87), (92, 93), (100, 101), (125, 126), (......False25882.00.0-24.9216490.5698011.03.0TrueTrueTrue
1692139.01.021.0{128, 0, 132, 4, 72, 153, 126}{11, 12, 13, 14, 15, 16, 17, 28, 29, 34, 35, 4...({128, 0, 132, 4, 72, 153, 126}, [{4, 5, 6, 7,...30.00.6272.0{(54, 55), (86, 87), (100, 101), (125, 126), (......False45641.00.06.7084310.6259991.03.0TrueTrueTrue
1702133.01.035.0{130, 138, 109, 114, 21, 150, 25, 126}{0, 1, 2, 3, 8, 23, 24, 28, 29, 32, 33, 38, 54...({130, 138, 109, 114, 21, 150, 25, 126}, [{0, ...30.00.5982.0{(86, 87), (125, 126), (156, 157), (40, 41), (......False24061.00.04.8096810.5980391.03.0TrueTrueTrue
1712153.01.032.0{128, 135, 137, 143, 16, 49, 50, 22}{0, 1, 130, 3, 2, 139, 30, 31, 36, 37, 39, 46,...({128, 135, 137, 143, 16, 49, 50, 22}, [{0, 1,...31.00.6282.0{(54, 55), (86, 87), (92, 93), (156, 157), (40......False62094.00.06.2145140.6264381.03.0TrueTrueTrue
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172 rows × 38 columns

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\n"," "]},"metadata":{},"execution_count":24}]},{"cell_type":"code","source":["df2 = pd.read_csv(df2_path)\n","df2.drop(['Unnamed: 0'], axis = 1, inplace = True, errors='ignore')\n","index = df2[(df2['Subject'] == 2155)].index\n","df2.drop(index , inplace=True)\n","df2"],"metadata":{"id":"EgNLUjvcaj2e","colab":{"base_uri":"https://localhost:8080/","height":956},"outputId":"c96f4290-3496-4a54-a070-43ad1da460ad"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Approximation and Heuristics Node Connectivity \\\n","0 2019.0 14.0 \n","1 2024.0 12.0 \n","2 2022.0 13.0 \n","3 2015.0 17.0 \n","4 2017.0 7.0 \n",".. ... ... \n","167 2157.0 11.0 \n","168 2162.0 12.0 \n","169 2139.0 9.0 \n","170 2133.0 17.0 \n","171 2153.0 12.0 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","0 {0, 4, 7, 137, 91, 11, 114, 19, 22, 123, 156, ... \n","1 {0, 162, 3, 8, 137, 59, 11, 48, 20, 22, 94, 15... \n","2 {0, 33, 5, 7, 138, 11, 142, 16, 18, 26, 59, 124} \n","3 {0, 1, 162, 99, 4, 135, 9, 11, 142, 50, 18, 60} \n","4 {129, 58, 39, 27, 13, 14, 145, 18, 51, 154, 59... \n",".. ... \n","167 {161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14... \n","168 {0, 129, 1, 99, 132, 4, 7, 136, 137, 138, 11, ... \n","169 {0, 39, 7, 11, 143, 18, 19, 30, 155, 60, 158} \n","170 {97, 163, 100, 4, 6, 142, 16, 18, 149, 121, 15... \n","171 {32, 0, 4, 137, 14, 143, 16, 89, 26, 157} \n","\n"," Approximation and Heuristics Max Cliques \\\n","0 {23, 27, 28, 31, 32, 33, 36, 37, 38, 39, 40, 4... \n","1 {97, 161, 7, 9, 106, 74, 138, 77, 10, 144, 146... \n","2 {0, 1, 2, 3, 73, 80, 48, 84, 85, 55, 87, 88, 1... \n","3 {8, 138, 10, 140, 141, 146, 147, 30, 31, 76, 7... \n","4 {64, 35, 4, 5, 6, 44, 109, 110, 45, 48, 81, 14... \n",".. ... \n","167 {160, 33, 32, 136, 8, 138, 139, 140, 146, 147,... \n","168 {97, 98, 101, 133, 103, 104, 106, 10, 76, 78, ... \n","169 {15, 16, 17, 21, 29, 34, 35, 44, 49, 68, 70, 7... \n","170 {23, 24, 25, 27, 28, 29, 32, 36, 38, 39, 40, 4... \n","171 {4, 5, 6, 13, 146, 21, 34, 44, 45, 64, 65, 66,... \n","\n"," Approximation and Heuristics Clique Removal \\\n","0 ({0, 4, 7, 137, 91, 11, 114, 19, 22, 123, 156,... \n","1 ({0, 162, 3, 8, 137, 59, 11, 48, 20, 22, 94, 1... \n","2 ({0, 33, 5, 7, 138, 11, 142, 16, 18, 26, 59, 1... \n","3 ({0, 1, 162, 99, 4, 135, 9, 11, 142, 50, 18, 6... \n","4 ({129, 58, 39, 27, 13, 14, 145, 18, 51, 154, 5... \n",".. ... \n","167 ({161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 1... \n","168 ({0, 129, 1, 99, 132, 4, 7, 136, 137, 138, 11,... \n","169 ({0, 39, 7, 11, 143, 18, 19, 30, 155, 60, 158}... \n","170 ({97, 163, 100, 4, 6, 142, 16, 18, 149, 121, 1... \n","171 ({32, 0, 4, 137, 14, 143, 16, 89, 26, 157}, [{... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 26.0 \n","1 21.0 \n","2 20.0 \n","3 24.0 \n","4 17.0 \n",".. ... \n","167 20.0 \n","168 17.0 \n","169 28.0 \n","170 25.0 \n","171 23.0 \n","\n"," Approximation and Heuristics Average Clustering \\\n","0 0.590 \n","1 0.491 \n","2 0.512 \n","3 0.574 \n","4 0.461 \n",".. ... \n","167 0.495 \n","168 0.453 \n","169 0.570 \n","170 0.550 \n","171 0.587 \n","\n"," Approximation and Heuristics Diameter \\\n","0 3.0 \n","1 3.0 \n","2 3.0 \n","3 3.0 \n","4 3.0 \n",".. ... \n","167 3.0 \n","168 3.0 \n","169 3.0 \n","170 3.0 \n","171 3.0 \n","\n"," Approximation and Heuristics Min Edge Dominating Set \\\n","0 {(54, 55), (125, 126), (17, 20), (40, 41), (72... \n","1 {(125, 126), (40, 41), (72, 73), (34, 35), (11... \n","2 {(86, 87), (154, 156), (18, 19), (127, 128), (... \n","3 {(54, 55), (125, 126), (72, 73), (34, 35), (10... \n","4 {(54, 55), (136, 141), (156, 157), (17, 20), (... \n",".. ... \n","167 {(125, 126), (40, 41), (18, 19), (34, 35), (23... \n","168 {(54, 55), (86, 87), (40, 41), (72, 73), (34, ... \n","169 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n","170 {(54, 55), (125, 126), (72, 73), (18, 19), (34... \n","171 {(86, 87), (92, 93), (156, 157), (72, 73), (18... \n","\n"," Approximation and Heuristics Min Wt Dominating Set ... Maximal Cliques \\\n","0 {131, 4, 133, 134, 6, 8, 9, 138, 139, 12, 13, ... ... 6311.0 \n","1 {0, 1, 2, 131, 133, 6, 5, 8, 138, 139, 144, 14... ... 3340.0 \n","2 {0, 2, 131, 4, 133, 14, 145, 146, 147, 17, 21,... ... 4121.0 \n","3 {5, 138, 10, 11, 144, 17, 30, 47, 64, 66, 73, ... ... 2932.0 \n","4 {128, 153, 131, 4, 5, 132, 6, 9, 10, 12, 144, ... ... 4570.0 \n",".. ... ... ... \n","167 {128, 133, 134, 7, 136, 9, 8, 12, 146, 147, 21... ... 4433.0 \n","168 {5, 134, 9, 140, 12, 13, 144, 17, 145, 20, 149... ... 2734.0 \n","169 {1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 15, 16, 17,... ... 5698.0 \n","170 {16, 17, 145, 23, 27, 28, 36, 37, 40, 43, 44, ... ... 5452.0 \n","171 {0, 6, 8, 9, 10, 139, 146, 147, 151, 29, 30, 3... ... 9187.0 \n","\n"," Num of isolates Non Randomness wrt Random Model Transitivity \\\n","0 0.0 13.402218 0.588124 \n","1 0.0 7.373402 0.503415 \n","2 0.0 -7.439670 0.511476 \n","3 0.0 -18.705485 0.580403 \n","4 0.0 7.005373 0.488998 \n",".. ... ... ... \n","167 0.0 -4.009700 0.499852 \n","168 0.0 3.327224 0.480864 \n","169 0.0 8.627942 0.566638 \n","170 0.0 6.700952 0.545750 \n","171 0.0 8.934200 0.561398 \n","\n"," Connected Components Diameter 1 Edge Connected 2 Edge Connected \\\n","0 1.0 3.0 True True \n","1 1.0 3.0 True True \n","2 1.0 3.0 True True \n","3 1.0 3.0 True True \n","4 1.0 3.0 True True \n",".. ... ... ... ... \n","167 1.0 3.0 True True \n","168 1.0 3.0 True True \n","169 1.0 3.0 True True \n","170 1.0 3.0 True True \n","171 1.0 3.0 True True \n","\n"," 3 Edge Connected Schizophrenic \n","0 True 0 \n","1 True 0 \n","2 True 0 \n","3 True 0 \n","4 True 0 \n",".. ... ... \n","167 True 1 \n","168 True 1 \n","169 True 1 \n","170 True 1 \n","171 True 1 \n","\n","[171 rows x 38 columns]"],"text/html":["\n","
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SubjectApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating SetApproximation and Heuristics Min Wt Dominating Set...Maximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge ConnectedSchizophrenic
02019.014.0{0, 4, 7, 137, 91, 11, 114, 19, 22, 123, 156, ...{23, 27, 28, 31, 32, 33, 36, 37, 38, 39, 40, 4...({0, 4, 7, 137, 91, 11, 114, 19, 22, 123, 156,...26.00.5903.0{(54, 55), (125, 126), (17, 20), (40, 41), (72...{131, 4, 133, 134, 6, 8, 9, 138, 139, 12, 13, ......6311.00.013.4022180.5881241.03.0TrueTrueTrue0
12024.012.0{0, 162, 3, 8, 137, 59, 11, 48, 20, 22, 94, 15...{97, 161, 7, 9, 106, 74, 138, 77, 10, 144, 146...({0, 162, 3, 8, 137, 59, 11, 48, 20, 22, 94, 1...21.00.4913.0{(125, 126), (40, 41), (72, 73), (34, 35), (11...{0, 1, 2, 131, 133, 6, 5, 8, 138, 139, 144, 14......3340.00.07.3734020.5034151.03.0TrueTrueTrue0
22022.013.0{0, 33, 5, 7, 138, 11, 142, 16, 18, 26, 59, 124}{0, 1, 2, 3, 73, 80, 48, 84, 85, 55, 87, 88, 1...({0, 33, 5, 7, 138, 11, 142, 16, 18, 26, 59, 1...20.00.5123.0{(86, 87), (154, 156), (18, 19), (127, 128), (...{0, 2, 131, 4, 133, 14, 145, 146, 147, 17, 21,......4121.00.0-7.4396700.5114761.03.0TrueTrueTrue0
32015.017.0{0, 1, 162, 99, 4, 135, 9, 11, 142, 50, 18, 60}{8, 138, 10, 140, 141, 146, 147, 30, 31, 76, 7...({0, 1, 162, 99, 4, 135, 9, 11, 142, 50, 18, 6...24.00.5743.0{(54, 55), (125, 126), (72, 73), (34, 35), (10...{5, 138, 10, 11, 144, 17, 30, 47, 64, 66, 73, ......2932.00.0-18.7054850.5804031.03.0TrueTrueTrue0
42017.07.0{129, 58, 39, 27, 13, 14, 145, 18, 51, 154, 59...{64, 35, 4, 5, 6, 44, 109, 110, 45, 48, 81, 14...({129, 58, 39, 27, 13, 14, 145, 18, 51, 154, 5...17.00.4613.0{(54, 55), (136, 141), (156, 157), (17, 20), (...{128, 153, 131, 4, 5, 132, 6, 9, 10, 12, 144, ......4570.00.07.0053730.4889981.03.0TrueTrueTrue0
..................................................................
1672157.011.0{161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14...{160, 33, 32, 136, 8, 138, 139, 140, 146, 147,...({161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 1...20.00.4953.0{(125, 126), (40, 41), (18, 19), (34, 35), (23...{128, 133, 134, 7, 136, 9, 8, 12, 146, 147, 21......4433.00.0-4.0097000.4998521.03.0TrueTrueTrue1
1682162.012.0{0, 129, 1, 99, 132, 4, 7, 136, 137, 138, 11, ...{97, 98, 101, 133, 103, 104, 106, 10, 76, 78, ...({0, 129, 1, 99, 132, 4, 7, 136, 137, 138, 11,...17.00.4533.0{(54, 55), (86, 87), (40, 41), (72, 73), (34, ...{5, 134, 9, 140, 12, 13, 144, 17, 145, 20, 149......2734.00.03.3272240.4808641.03.0TrueTrueTrue1
1692139.09.0{0, 39, 7, 11, 143, 18, 19, 30, 155, 60, 158}{15, 16, 17, 21, 29, 34, 35, 44, 49, 68, 70, 7...({0, 39, 7, 11, 143, 18, 19, 30, 155, 60, 158}...28.00.5703.0{(54, 55), (86, 87), (100, 101), (125, 126), (...{1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 15, 16, 17,......5698.00.08.6279420.5666381.03.0TrueTrueTrue1
1702133.017.0{97, 163, 100, 4, 6, 142, 16, 18, 149, 121, 15...{23, 24, 25, 27, 28, 29, 32, 36, 38, 39, 40, 4...({97, 163, 100, 4, 6, 142, 16, 18, 149, 121, 1...25.00.5503.0{(54, 55), (125, 126), (72, 73), (18, 19), (34...{16, 17, 145, 23, 27, 28, 36, 37, 40, 43, 44, ......5452.00.06.7009520.5457501.03.0TrueTrueTrue1
1712153.012.0{32, 0, 4, 137, 14, 143, 16, 89, 26, 157}{4, 5, 6, 13, 146, 21, 34, 44, 45, 64, 65, 66,...({32, 0, 4, 137, 14, 143, 16, 89, 26, 157}, [{...23.00.5873.0{(86, 87), (92, 93), (156, 157), (72, 73), (18...{0, 6, 8, 9, 10, 139, 146, 147, 151, 29, 30, 3......9187.00.08.9342000.5613981.03.0TrueTrueTrue1
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171 rows × 38 columns

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\n"," "]},"metadata":{},"execution_count":25}]},{"cell_type":"code","source":["df3 = pd.read_csv(df3_path)\n","df3.drop(['Unnamed: 0'], axis = 1, inplace = True, errors='ignore')\n","bad_sub = [2068, 2033, 2108, 2082, 2155, 2163, 2134, 2154, 2168]\n","index = df3[(df3['Subject'] == 2068) | (df3['Subject'] == 2033) | (df3['Subject'] == 2168) | (df3['Subject'] == 2014) | (df3['Subject'] == 2003) | (df3['Subject'] == 2024) | (df3['Subject'] == 2108) | (df3['Subject'] == 2082) | (df3['Subject'] == 2155) | (df3['Subject'] == 2163) | (df3['Subject'] == 2134) | (df3['Subject'] == 2154)].index\n","df3.drop(index , inplace=True)\n","df3"],"metadata":{"id":"2cVGQpc9bAIS","colab":{"base_uri":"https://localhost:8080/","height":922},"outputId":"828bf3ba-fbf5-46f0-dc9e-d3c3542a5910"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Approximation and Heuristics Node Connectivity \\\n","0 2019.0 5.0 \n","1 2022.0 3.0 \n","2 2015.0 6.0 \n","3 2025.0 1.0 \n","4 2017.0 3.0 \n",".. ... ... \n","164 2157.0 4.0 \n","165 2139.0 1.0 \n","166 2127.0 5.0 \n","167 2133.0 7.0 \n","168 2153.0 3.0 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","0 {0, 129, 1, 3, 6, 137, 142, 18, 148, 149, 26, ... \n","1 {129, 130, 1, 132, 7, 8, 138, 11, 142, 16, 18,... \n","2 {130, 135, 142, 145, 18, 19, 149, 155, 28, 162... \n","3 {128, 6, 135, 137, 15, 18, 22, 27, 155, 156, 3... \n","4 {0, 129, 1, 4, 7, 139, 11, 142, 14, 18, 149, 2... \n",".. ... \n","164 {0, 1, 6, 7, 11, 12, 13, 142, 15, 154, 36, 49,... \n","165 {128, 0, 4, 6, 135, 136, 8, 138, 11, 142, 18, ... \n","166 {129, 5, 6, 136, 10, 13, 142, 16, 19, 22, 154,... \n","167 {128, 163, 8, 11, 142, 110, 16, 115, 83, 52, 5... \n","168 {129, 1, 131, 8, 11, 12, 142, 18, 23, 152, 29,... \n","\n"," Approximation and Heuristics Max Cliques \\\n","0 {32, 33, 2, 36, 37, 38, 39, 71, 73, 140, 85, 2... \n","1 {64, 65, 4, 5, 6, 44, 109, 110, 45, 49, 51, 11... \n","2 {66, 8, 9, 138, 139, 76, 77, 10, 146, 147, 30,... \n","3 {0, 1, 2, 3, 39, 72, 73, 14, 87, 88} \n","4 {97, 98, 7, 8, 105, 106, 10, 76, 9, 150, 121, ... \n",".. ... \n","164 {32, 33, 38, 136, 140, 141, 146, 147, 150, 152... \n","165 {5, 12, 13, 15, 16, 17, 28, 29, 34, 49, 53, 71... \n","166 {3, 8, 138, 139, 140, 141, 144, 146, 147, 151,... \n","167 {32, 129, 38, 71, 72, 73, 42, 107, 40, 17, 84,... \n","168 {160, 98, 90, 103, 8, 105, 106, 9, 76, 77, 7, ... \n","\n"," Approximation and Heuristics Clique Removal \\\n","0 ({0, 129, 1, 3, 6, 137, 142, 18, 148, 149, 26,... \n","1 ({129, 130, 1, 132, 7, 8, 138, 11, 142, 16, 18... \n","2 ({130, 135, 142, 145, 18, 19, 149, 155, 28, 16... \n","3 ({128, 6, 135, 137, 15, 18, 22, 27, 155, 156, ... \n","4 ({0, 129, 1, 4, 7, 139, 11, 142, 14, 18, 149, ... \n",".. ... \n","164 ({0, 1, 6, 7, 11, 12, 13, 142, 15, 154, 36, 49... \n","165 ({128, 0, 4, 6, 135, 136, 8, 138, 11, 142, 18,... \n","166 ({129, 5, 6, 136, 10, 13, 142, 16, 19, 22, 154... \n","167 ({128, 163, 8, 11, 142, 110, 16, 115, 83, 52, ... \n","168 ({129, 1, 131, 8, 11, 12, 142, 18, 23, 152, 29... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 19.0 \n","1 14.0 \n","2 19.0 \n","3 12.0 \n","4 15.0 \n",".. ... \n","164 16.0 \n","165 22.0 \n","166 30.0 \n","167 19.0 \n","168 18.0 \n","\n"," Approximation and Heuristics Average Clustering \\\n","0 0.567 \n","1 0.458 \n","2 0.549 \n","3 0.470 \n","4 0.429 \n",".. ... \n","164 0.477 \n","165 0.528 \n","166 0.610 \n","167 0.544 \n","168 0.518 \n","\n"," Approximation and Heuristics Diameter \\\n","0 4.0 \n","1 4.0 \n","2 3.0 \n","3 4.0 \n","4 4.0 \n",".. ... \n","164 4.0 \n","165 3.0 \n","166 4.0 \n","167 3.0 \n","168 4.0 \n","\n"," Approximation and Heuristics Min Edge Dominating Set \\\n","0 {(125, 126), (40, 41), (72, 73), (153, 160), (... \n","1 {(156, 157), (127, 128), (113, 114), (140, 148... \n","2 {(6, 9), (54, 55), (62, 64), (125, 126), (134,... \n","3 {(30, 65), (125, 126), (154, 156), (33, 36), (... \n","4 {(54, 55), (86, 87), (100, 101), (125, 126), (... \n",".. ... \n","164 {(57, 61), (100, 101), (40, 41), (72, 73), (34... \n","165 {(92, 93), (100, 101), (125, 126), (122, 131),... \n","166 {(54, 55), (125, 126), (21, 28), (33, 36), (34... \n","167 {(6, 9), (125, 126), (26, 28), (68, 76), (18, ... \n","168 {(54, 55), (86, 87), (125, 126), (72, 73), (34... \n","\n"," Approximation and Heuristics Min Wt Dominating Set ... Maximal Cliques \\\n","0 {4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17,... ... 2178.0 \n","1 {0, 2, 131, 4, 133, 6, 12, 13, 17, 145, 147, 1... ... 1105.0 \n","2 {0, 1, 2, 128, 5, 6, 7, 8, 9, 10, 138, 12, 13,... ... 1008.0 \n","3 {0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 1... ... 1059.0 \n","4 {1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16, 17, 19, ... ... 1029.0 \n",".. ... ... ... \n","164 {128, 4, 133, 134, 7, 8, 136, 138, 10, 6, 146,... ... 1161.0 \n","165 {1, 2, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16,... ... 1586.0 \n","166 {1, 2, 3, 7, 8, 9, 138, 139, 140, 141, 11, 14,... ... 1671.0 \n","167 {129, 2, 3, 1, 7, 9, 11, 12, 16, 17, 144, 23, ... ... 1725.0 \n","168 {0, 1, 2, 4, 6, 8, 9, 10, 12, 13, 14, 15, 16, ... ... 2568.0 \n","\n"," Num of isolates Non Randomness wrt Random Model Transitivity \\\n","0 0.0 16.229224 0.555217 \n","1 0.0 1.068700 0.474974 \n","2 0.0 3.795201 0.559561 \n","3 0.0 -5.157916 0.437976 \n","4 0.0 10.166776 0.453146 \n",".. ... ... ... \n","164 0.0 4.265055 0.447614 \n","165 0.0 12.235447 0.528256 \n","166 0.0 1.166344 0.625417 \n","167 0.0 12.227727 0.516497 \n","168 0.0 11.727501 0.519539 \n","\n"," Connected Components Diameter 1 Edge Connected 2 Edge Connected \\\n","0 1.0 4.0 True True \n","1 1.0 4.0 True True \n","2 1.0 4.0 True True \n","3 1.0 4.0 True False \n","4 1.0 4.0 True True \n",".. ... ... ... ... \n","164 1.0 4.0 True True \n","165 1.0 4.0 True False \n","166 1.0 4.0 True True \n","167 1.0 3.0 True True \n","168 1.0 4.0 True True \n","\n"," 3 Edge Connected Schizophrenic \n","0 True 0.0 \n","1 True 0.0 \n","2 True 0.0 \n","3 False 0.0 \n","4 True 0.0 \n",".. ... ... \n","164 True 1.0 \n","165 False 1.0 \n","166 True 1.0 \n","167 True 1.0 \n","168 True 1.0 \n","\n","[160 rows x 38 columns]"],"text/html":["\n","
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SubjectApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating SetApproximation and Heuristics Min Wt Dominating Set...Maximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge ConnectedSchizophrenic
02019.05.0{0, 129, 1, 3, 6, 137, 142, 18, 148, 149, 26, ...{32, 33, 2, 36, 37, 38, 39, 71, 73, 140, 85, 2...({0, 129, 1, 3, 6, 137, 142, 18, 148, 149, 26,...19.00.5674.0{(125, 126), (40, 41), (72, 73), (153, 160), (...{4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17,......2178.00.016.2292240.5552171.04.0TrueTrueTrue0.0
12022.03.0{129, 130, 1, 132, 7, 8, 138, 11, 142, 16, 18,...{64, 65, 4, 5, 6, 44, 109, 110, 45, 49, 51, 11...({129, 130, 1, 132, 7, 8, 138, 11, 142, 16, 18...14.00.4584.0{(156, 157), (127, 128), (113, 114), (140, 148...{0, 2, 131, 4, 133, 6, 12, 13, 17, 145, 147, 1......1105.00.01.0687000.4749741.04.0TrueTrueTrue0.0
22015.06.0{130, 135, 142, 145, 18, 19, 149, 155, 28, 162...{66, 8, 9, 138, 139, 76, 77, 10, 146, 147, 30,...({130, 135, 142, 145, 18, 19, 149, 155, 28, 16...19.00.5493.0{(6, 9), (54, 55), (62, 64), (125, 126), (134,...{0, 1, 2, 128, 5, 6, 7, 8, 9, 10, 138, 12, 13,......1008.00.03.7952010.5595611.04.0TrueTrueTrue0.0
32025.01.0{128, 6, 135, 137, 15, 18, 22, 27, 155, 156, 3...{0, 1, 2, 3, 39, 72, 73, 14, 87, 88}({128, 6, 135, 137, 15, 18, 22, 27, 155, 156, ...12.00.4704.0{(30, 65), (125, 126), (154, 156), (33, 36), (...{0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 1......1059.00.0-5.1579160.4379761.04.0TrueFalseFalse0.0
42017.03.0{0, 129, 1, 4, 7, 139, 11, 142, 14, 18, 149, 2...{97, 98, 7, 8, 105, 106, 10, 76, 9, 150, 121, ...({0, 129, 1, 4, 7, 139, 11, 142, 14, 18, 149, ...15.00.4294.0{(54, 55), (86, 87), (100, 101), (125, 126), (...{1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16, 17, 19, ......1029.00.010.1667760.4531461.04.0TrueTrueTrue0.0
..................................................................
1642157.04.0{0, 1, 6, 7, 11, 12, 13, 142, 15, 154, 36, 49,...{32, 33, 38, 136, 140, 141, 146, 147, 150, 152...({0, 1, 6, 7, 11, 12, 13, 142, 15, 154, 36, 49...16.00.4774.0{(57, 61), (100, 101), (40, 41), (72, 73), (34...{128, 4, 133, 134, 7, 8, 136, 138, 10, 6, 146,......1161.00.04.2650550.4476141.04.0TrueTrueTrue1.0
1652139.01.0{128, 0, 4, 6, 135, 136, 8, 138, 11, 142, 18, ...{5, 12, 13, 15, 16, 17, 28, 29, 34, 49, 53, 71...({128, 0, 4, 6, 135, 136, 8, 138, 11, 142, 18,...22.00.5283.0{(92, 93), (100, 101), (125, 126), (122, 131),...{1, 2, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16,......1586.00.012.2354470.5282561.04.0TrueFalseFalse1.0
1662127.05.0{129, 5, 6, 136, 10, 13, 142, 16, 19, 22, 154,...{3, 8, 138, 139, 140, 141, 144, 146, 147, 151,...({129, 5, 6, 136, 10, 13, 142, 16, 19, 22, 154...30.00.6104.0{(54, 55), (125, 126), (21, 28), (33, 36), (34...{1, 2, 3, 7, 8, 9, 138, 139, 140, 141, 11, 14,......1671.00.01.1663440.6254171.04.0TrueTrueTrue1.0
1672133.07.0{128, 163, 8, 11, 142, 110, 16, 115, 83, 52, 5...{32, 129, 38, 71, 72, 73, 42, 107, 40, 17, 84,...({128, 163, 8, 11, 142, 110, 16, 115, 83, 52, ...19.00.5443.0{(6, 9), (125, 126), (26, 28), (68, 76), (18, ...{129, 2, 3, 1, 7, 9, 11, 12, 16, 17, 144, 23, ......1725.00.012.2277270.5164971.03.0TrueTrueTrue1.0
1682153.03.0{129, 1, 131, 8, 11, 12, 142, 18, 23, 152, 29,...{160, 98, 90, 103, 8, 105, 106, 9, 76, 77, 7, ...({129, 1, 131, 8, 11, 12, 142, 18, 23, 152, 29...18.00.5184.0{(54, 55), (86, 87), (125, 126), (72, 73), (34...{0, 1, 2, 4, 6, 8, 9, 10, 12, 13, 14, 15, 16, ......2568.00.011.7275010.5195391.04.0TrueTrueTrue1.0
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160 rows × 38 columns

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\n"," "]},"metadata":{},"execution_count":26}]},{"cell_type":"code","source":["dfs = [df3]"],"metadata":{"id":"h_Ei8TfNdW9c"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# DATA CLEANING"],"metadata":{"id":"HeIxk4kqcjl2"}},{"cell_type":"code","source":["for df in dfs:\n"," # nested structures\n"," df.drop(['Approximation and Heuristics Clique Removal','Approximation and Heuristics Min Edge Dominating Set', 'Approximation and Heuristics Maximal Matching',\n"," 'Approximation and Heuristics Ramsay', 'Approximation and Heuristics treewidth Min Wt Vertex Cover'], axis=1, errors = 'ignore', inplace=True)\n"," # sets/lists\n"," df['Approximation and Heuristics Max Independent Sets'] = len(df['Approximation and Heuristics Max Independent Sets'])\n"," df['Asteroidal Triple']= len(df['Asteroidal Triple'])\n"," df['Approximation and Heuristics Max Cliques'] = len(df['Approximation and Heuristics Max Cliques'])\n"," df['Approximation and Heuristics TSP'] = len(df['Approximation and Heuristics TSP'])\n"," df['Approximation and Heuristics Diameter'] = len(df['Approximation and Heuristics Diameter'])\n"," df['Approximation and Heuristics Min Wt Dominating Set'] = len(df['Approximation and Heuristics Min Wt Dominating Set'])\n"," df['Approximation and Heuristics Randomized Partitioning'] = df['Approximation and Heuristics Randomized Partitioning'].apply(lambda k: eval(k)).apply(lambda k: k[0])\n"," df['Approximation and Heuristics One Exchange'] = df['Approximation and Heuristics One Exchange'].apply(lambda k: eval(k)).apply(lambda k: k[0])\n","\n"," # bool to num\n"," df['1 Edge Connected'] = df['1 Edge Connected'].map({True:1 ,False:0})\n"," df['2 Edge Connected'] = df['2 Edge Connected'].map({True:1 ,False:0})\n"," df['3 Edge Connected'] = df['3 Edge Connected'].map({True:1 ,False:0})\n"," df['Bridges'] = df['Bridges'].map({True:1 ,False:0})\n"," df['Chordal'] = df['Chordal'].map({True:1 ,False:0})\n","\n"," print(df.shape)"],"metadata":{"id":"JDCinmtSckxC","colab":{"base_uri":"https://localhost:8080/"},"outputId":"644b4c0a-e0e6-4771-d3a7-90d906d44927"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["(160, 33)\n"]}]},{"cell_type":"markdown","source":["**Non unique columns**"],"metadata":{"id":"u4rbQgqWfNj0"}},{"cell_type":"code","source":["for df in dfs:\n"," for col in df.columns:\n"," if len(df[col].unique()) == 1:\n"," df.drop([col], axis=1, inplace=True)\n"," print(df.shape)"],"metadata":{"id":"TfdikAoPd_Dw","colab":{"base_uri":"https://localhost:8080/"},"outputId":"67438a61-45c7-4b56-bdce-edb3d0788984"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["(160, 23)\n"]}]},{"cell_type":"markdown","source":["# TEST TRAIN SPLIT"],"metadata":{"id":"RkgR-AHifmHo"}},{"cell_type":"code","source":["def preprocessing_pipeline(X):\n"," return X"],"metadata":{"id":"Q27iuywrkQhI"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["def split_fn(df):\n"," X = df.drop(['Schizophrenic','Subject'], axis=1)\n"," y = df['Schizophrenic']\n","\n"," return X, y"],"metadata":{"id":"eWtyaiVcfnS6"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["def main(df, clf, param):\n"," # data\n"," X, y = split_fn(df)\n"," X = preprocessing_pipeline(X)\n","\n"," # grid\n"," gscv = GridSearchCV(clf, param)\n"," gscv.fit(X, y)\n"," return gscv"],"metadata":{"id":"weeq2BAXqKcZ"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["clf = XGBClassifier(learning_rate=0.02, objective='binary:logistic', silent=True, nthread=2)\n","\n","\n","parameters = {\n"," 'loss': ['log_loss', 'exponential'],\n"," 'max_depth': range (2, 50, 1),\n"," 'n_estimators': range(5, 300, 50)\n","}"],"metadata":{"id":"HQnPSSp8r_eT"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["res = []\n","for df in dfs: \n"," res.append(main(df, clf, parameters))"],"metadata":{"id":"cwnojbHCv2sK"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for clf in res:\n"," print(clf.best_estimator_)\n"," print(clf.best_params_)\n"," print(clf.best_score_)\n"," print()"],"metadata":{"id":"VWwCP9HsBN07","colab":{"base_uri":"https://localhost:8080/"},"outputId":"af635d23-b8c7-40c5-ca7c-e6d63d5171bd"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["XGBClassifier(learning_rate=0.02, loss='log_loss', max_depth=2, n_estimators=5,\n"," nthread=2, silent=True)\n","{'loss': 'log_loss', 'max_depth': 2, 'n_estimators': 5}\n","0.74375\n","\n"]}]}]} \ No newline at end of file diff --git a/Code/3. Data Augmentation/Data Augmentation Distribution sampling.ipynb b/Code/3. Data Augmentation/Data Augmentation Distribution sampling.ipynb new file mode 100644 index 0000000..c6e8875 --- /dev/null +++ b/Code/3. Data Augmentation/Data Augmentation Distribution sampling.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"code","source":["!pip install fitter"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"M5jwUpFiCCIz","outputId":"17a4ecda-f886-4a9a-83a1-774aea420b0b"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Collecting fitter\n"," Downloading fitter-1.5.1.tar.gz (27 kB)\n","Requirement already satisfied: click in /usr/local/lib/python3.7/dist-packages (from fitter) (7.1.2)\n","Requirement already satisfied: joblib in /usr/local/lib/python3.7/dist-packages (from fitter) (1.1.0)\n","Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from fitter) (3.2.2)\n","Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from fitter) (1.21.6)\n","Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from fitter) (1.3.5)\n","Requirement already satisfied: scipy>=0.18 in /usr/local/lib/python3.7/dist-packages (from fitter) (1.7.3)\n","Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from fitter) (4.64.1)\n","Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->fitter) (1.4.4)\n","Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->fitter) (2.8.2)\n","Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->fitter) (3.0.9)\n","Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->fitter) (0.11.0)\n","Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from kiwisolver>=1.0.1->matplotlib->fitter) (4.1.1)\n","Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.1->matplotlib->fitter) (1.15.0)\n","Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas->fitter) (2022.2.1)\n","Building wheels for collected packages: fitter\n"," Building wheel for fitter (setup.py) ... \u001b[?25l\u001b[?25hdone\n"," Created wheel for fitter: filename=fitter-1.5.1-py3-none-any.whl size=25596 sha256=2f4689e4e2044e8bf5e840ff7ce13afff26a49d0d33ced3df7aad46e796dd990\n"," Stored in directory: /root/.cache/pip/wheels/40/65/62/57b872ba7af36e70111b1f67cffe76f97c747804aff7665ccb\n","Successfully built fitter\n","Installing collected packages: fitter\n","Successfully installed fitter-1.5.1\n"]}]},{"cell_type":"code","execution_count":null,"metadata":{"id":"kohVVflp6Q34"},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","from google.colab import files\n","import os\n","import networkx as nx\n","import seaborn as sns\n","from fitter import Fitter, get_common_distributions, get_distributions\n","import random\n","import os"]},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"sOcq6vWO7bU3","outputId":"794509d4-9bca-491d-b447-59b037277d2b"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"]}]},{"cell_type":"code","source":["ucla_v2 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","ucla_v2_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Aug Weighted'"],"metadata":{"id":"16M6PD8vhwOo"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Method 1: Random Sampling"],"metadata":{"id":"UvCLBVVX9u9T"}},{"cell_type":"code","source":["for sample in os.listdir(ucla_weighted):\n"," if '(' in sample:\n"," continue\n"," if(sample.endswith('.csv')): \n"," file=ucla_weighted+ '/' +sample\n"," data=pd.read_csv(file, header=None)\n"," data= data.fillna(0)\n"," df= data.to_numpy()\n"," for i in range(swaps):\n"," i=randint(0,163)\n"," j=randint(0,163)\n"," val=np.median(df[i])\n"," df[i][j]=val\n"," df[j][i]= val\n","\n"," df1= pd.DataFrame(df, columns=data.columns)\n"," dest_file = 'ucla_weighted_'+ str(subject) +'.csv'\n"," try:\n"," df1.to_csv( dest_dir+dest_file, index=False, header=False, encoding = 'utf-8') \n"," except Exception as e:\n"," print(e)\n"," subject+=1"],"metadata":{"id":"qjgjIS_I9uUe"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Distributed Sampling"],"metadata":{"id":"lgpa8fo99xSy"}},{"cell_type":"code","source":["def augment(np_v2_2, col, row):\n"," indx = random.sample(range(0, col), 7)\n"," indy = random.sample(range(0, row), 7)\n"," for i in range(len(indx)):\n"," s = random.sample(range(0, 1), 1)\n"," r = random.uniform(0,0.3)\n"," if s==0:\n"," np_v2_2[indx[i]][indy[i]] = r + np_v2_2[indx[i]][indy[i]]\n"," np_v2_2[indy[i]] [indx[i]] = r + np_v2_2[indy[i]][indx[i]]\n"," else:\n"," np_v2_2[indx[i]][indy[i]] = r - np_v2_2[indx[i]][indy[i]]\n"," np_v2_2[indy[i]] [indx[i]] = r - np_v2_2[indy[i]][indx[i]]\n"," return np_v2_2"],"metadata":{"id":"uDtRO9Mdit6s"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for f in os.listdir(ucla_v2):\n"," if '(' in f:\n"," continue\n"," if not f.endswith('csv'):\n"," continue\n"," ucla_v2_sub = os.path.join(ucla_v2, f)\n"," #print(ucla_v2_sub)\n"," df_v2_sub = pd.read_csv(ucla_v2_sub, header=None)\n"," col = len(df_v2_sub)\n"," row = len(df_v2_sub[0])\n"," df_v2_aug = augment(df_v2_sub, col, row)\n"," h = f.rfind('_')\n"," p = f.find('.')\n"," sub_name = int(f[h+1:p])+1000\n"," file_name = 'ucla_weighted'+'_'+str(sub_name)+'.csv'\n"," dest = os.path.join(ucla_v2_aug, file_name)\n"," try:\n"," df_v2_aug.to_csv(dest, index=False, header=False, encoding = 'utf-8') \n"," except:\n"," print(\"ERROR: Create a folder having this path:\",dest) \n"," break"],"metadata":{"id":"_DxV7AJMhwMM"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Extra Trial"],"metadata":{"id":"MjlJhhfYq2MR"}},{"cell_type":"code","source":["ucla_v2_2001 ='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2/ucla_weighted_2001.csv'\n","\n","df_v2 = pd.read_csv(ucla_v2_2001, header=None)\n","df_v2.head()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":300},"id":"ujtx38248a4c","outputId":"6d3e151a-ba3c-4347-bb2a-3130714d16d3"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" 0 1 2 3 4 5 6 \\\n","0 NaN 0.408635 0.091122 0.141027 0.212356 0.232217 0.153159 \n","1 0.408635 NaN 0.437967 0.452820 -0.194418 -0.061455 0.120086 \n","2 0.091122 0.437967 NaN 0.149192 -0.210396 -0.088659 -0.010411 \n","3 0.141027 0.452820 0.149192 NaN -0.279202 -0.365347 0.139110 \n","4 0.212356 -0.194418 -0.210396 -0.279202 NaN 1.230418 0.292630 \n","\n"," 7 8 9 ... 154 155 156 157 \\\n","0 0.101704 0.422963 0.128853 ... -0.025669 -0.193461 -0.301842 0.016608 \n","1 -0.040434 0.113105 -0.100684 ... 0.074928 0.391174 -0.152202 0.013005 \n","2 -0.142276 0.162457 0.029971 ... 0.170891 0.203254 -0.453497 -0.228100 \n","3 -0.151724 -0.135375 -0.234444 ... 0.220136 0.406015 -0.007174 0.287492 \n","4 0.114947 -0.027004 0.126552 ... -0.102763 -0.168673 -0.215468 -0.067362 \n","\n"," 158 159 160 161 162 163 \n","0 0.125022 0.127793 -0.009022 0.032929 -0.287735 -0.032206 \n","1 0.098310 -0.119852 0.071226 -0.041300 0.020607 0.334697 \n","2 -0.106776 -0.055199 0.002006 -0.092069 0.141708 0.123455 \n","3 0.414779 -0.405352 -0.256749 -0.123936 0.341234 0.212942 \n","4 0.078732 0.172673 -0.104079 0.324740 0.002076 0.071211 \n","\n","[5 rows x 164 columns]"],"text/html":["\n","
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10.408635NaN0.4379670.452820-0.194418-0.0614550.120086-0.0404340.113105-0.100684...0.0749280.391174-0.1522020.0130050.098310-0.1198520.071226-0.0413000.0206070.334697
20.0911220.437967NaN0.149192-0.210396-0.088659-0.010411-0.1422760.1624570.029971...0.1708910.203254-0.453497-0.228100-0.106776-0.0551990.002006-0.0920690.1417080.123455
30.1410270.4528200.149192NaN-0.279202-0.3653470.139110-0.151724-0.135375-0.234444...0.2201360.406015-0.0071740.2874920.414779-0.405352-0.256749-0.1239360.3412340.212942
40.212356-0.194418-0.210396-0.279202NaN1.2304180.2926300.114947-0.0270040.126552...-0.102763-0.168673-0.215468-0.0673620.0787320.172673-0.1040790.3247400.0020760.071211
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5 rows × 164 columns

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sumsquare_erroraicbickl_divks_statisticks_pvalue
beta1.184787419.197755-6710.560827inf0.0253030.535436
norm1.200274416.899778-6711.389748inf0.0286250.378500
lognorm1.209820420.913752-6696.560377inf0.0306860.297040
gamma1.215311420.685136-6692.031856inf0.0313330.274229
burr2.257951517.038813-6065.666492inf0.0739030.000034
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\n"," "]},"metadata":{},"execution_count":42},{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":["for i in range(col):\n"," l = []\n"," for j in range(row):\n"," if np_v2[j][i] != np.nan:\n"," l.append(np_v2[j][i])\n"," print(l)\n"," try:\n"," f = Fitter(l,\n"," distributions=['gamma',\n"," 'lognorm',\n"," \"beta\",\n"," \"burr\",\n"," \"norm\"])\n"," f.fit()\n"," f.summary()\n"," dist = f.get_best(method = 'sumsquare_error')\n"," print(dist)\n"," mean = dist[0][0]\n"," stdev = dist[0][1]\n"," data = np.random.normal(mean, stdev, 5)\n"," ind = random.sample(range(1, col), 5)\n"," for idx in range(len(ind)):\n"," np_v2[i][ind[idx]] = data[idx]\n"," except:\n"," count+=1\n"," pass"],"metadata":{"id":"_mYXgyb3AFDQ"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for i in range(col):\n"," l = []\n"," for j in range(row):\n"," if np_v2[j][i] != np.nan:\n"," l.append(np_v2[j][i])\n"," print(l)\n"," data = random.sample(l, 5)\n"," ind = random.sample(range(1, col), 5)\n"," for idx in range(len(ind)):\n"," np_v2[ind[idx]][i] = data[idx]"],"metadata":{"id":"eEv9wghaMB7A"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["indx = random.sample(range(0, row), 7)\n","indy = random.sample(range(0, col), 7)\n","for i in range(len(indx)):\n"," s = random.sample(range(0, 1), 1)\n"," r = random.uniform(0,0.3)\n"," if s==0:\n"," np_v2_2[indx[i]][indy[i]] = r + np_v2_2[indx[i]][indy[i]]\n"," else:\n"," np_v2_2[indx[i]][indy[i]] = r - np_v2_2[indx[i]][indy[i]]\n","\n","for i in range(len(indx)):\n"," s = random.sample(range(0, 1), 1)\n"," r = random.uniform(0,0.3)\n"," if s==0:\n"," np_v2_2[indy[i]] [indx[i]] = r + np_v2_2[indy[i]][indx[i]]\n"," else:\n"," np_v2_2[indy[i]] [indx[i]] = r - np_v2_2[indy[i]][indx[i]]"],"metadata":{"id":"jIBvpbb4dC8C"},"execution_count":null,"outputs":[]}]} \ No newline at end of file diff --git a/Code/4. Machine Learning/All ML Models 10 fold CV.ipynb b/Code/4. Machine Learning/All ML Models 10 fold CV.ipynb new file mode 100644 index 0000000..ea8c972 --- /dev/null +++ b/Code/4. Machine Learning/All ML Models 10 fold CV.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# IMPORT"],"metadata":{"id":"Ipf2gJ0dRMjb"}},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nQOVc2CdRpNd","outputId":"cf232105-ee9a-4d71-9c57-26d9e32f24ac","executionInfo":{"status":"ok","timestamp":1671363740437,"user_tz":-330,"elapsed":27728,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9R8R0jALQ_7H"},"outputs":[],"source":["import pandas as pd \n","import numpy as np\n","import statistics\n","from sklearn import preprocessing,svm\n","from sklearn.metrics import *\n","from sklearn.neighbors import KNeighborsRegressor\n","from sklearn.preprocessing import StandardScaler, Normalizer, MinMaxScaler\n","from itertools import product, combinations\n","from sklearn.ensemble import AdaBoostClassifier\n","from sklearn.tree import DecisionTreeClassifier\n","from sklearn.linear_model import LogisticRegression\n","from sklearn.neighbors import KNeighborsClassifier\n","from sklearn.svm import SVC\n","from sklearn.model_selection import GridSearchCV, cross_val_score, StratifiedKFold, train_test_split, LeaveOneOut, RepeatedStratifiedKFold\n","import itertools\n","import matplotlib.pyplot as plt\n","from sklearn.pipeline import Pipeline\n","import cvxopt\n","import matplotlib.mlab as mlab\n","import seaborn\n","import pickle\n","\n","from sklearn.metrics import f1_score, accuracy_score, recall_score, precision_score\n","import warnings\n","warnings.filterwarnings(\"ignore\")\n","%matplotlib inline"]},{"cell_type":"markdown","source":["# DATA LOADING"],"metadata":{"id":"FO2_ByN3Rp7E"}},{"cell_type":"code","source":["df2_gb = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Global features/global_measures_binary_combined_0_2.csv'\n","df2_gw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Global features/global_combined_weighted.csv'"],"metadata":{"id":"m6T6JlieZduW"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df2 = pd.read_csv(df2_gb)\n","df2.drop(['Unnamed: 0',], axis = 1, inplace = True, errors='ignore')\n","index = df2[(df2['Subject'] == 2155)].index\n","df2.drop(index , inplace=True)\n","df2"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":939},"id":"EgNLUjvcaj2e","outputId":"d0a72869-8dff-443a-f279-8225af38186d","executionInfo":{"status":"ok","timestamp":1671363796337,"user_tz":-330,"elapsed":1064,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Schizophrenic Approximation and Heuristics Node Connectivity \\\n","0 2001 0 10 \n","1 2002 0 11 \n","2 2003 0 1 \n","3 2004 0 10 \n","4 2005 0 15 \n",".. ... ... ... \n","238 4156 1 11 \n","239 4159 1 12 \n","240 4169 1 5 \n","241 4170 1 6 \n","242 4171 1 8 \n","\n"," Approximation and Heuristics Max Independent Sets \\\n","0 {160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 14... \n","1 {0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93, 94} \n","2 {96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24,... \n","3 {4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61,... \n","4 {0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 15... \n",".. ... \n","238 {161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14... \n","239 {160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 11... \n","240 {130, 132, 133, 100, 137, 74, 42, 11, 141, 143... \n","241 NaN \n","242 {32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58, ... \n","\n"," Approximation and Heuristics Max Cliques \\\n","0 {32, 33, 2, 38, 72, 73, 43, 140, 148, 149, 22,... \n","1 {12, 14, 15, 145, 146, 17, 158, 34, 35, 36, 68... \n","2 {32, 34, 68, 36, 70, 40, 42, 107, 13, 111, 16,... \n","3 {64, 102, 103, 104, 46, 50, 51, 52, 54, 58, 29} \n","4 {128, 0, 131, 132, 133, 134, 136, 11, 83, 84, ... \n",".. ... \n","238 {160, 33, 32, 136, 8, 138, 139, 140, 146, 147,... \n","239 {132, 5, 6, 7, 4, 9, 34, 35, 45, 46, 64, 65, 7... \n","240 {64, 65, 4, 5, 6, 7, 9, 44, 45, 112, 81, 116, ... \n","241 {11, 12, 13, 14, 15, 144, 24, 27, 29, 32, 33, ... \n","242 {4, 133, 134, 7, 6, 9, 5, 145, 34, 35, 44, 45,... \n","\n"," Approximation and Heuristics Clique Removal \\\n","0 ({160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 1... \n","1 ({0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93,... \n","2 ({96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24... \n","3 ({4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61... \n","4 ({0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 1... \n",".. ... \n","238 ({161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 1... \n","239 ({160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 1... \n","240 ({130, 132, 133, 100, 137, 74, 42, 11, 141, 14... \n","241 ({161, 1, 4, 7, 16, 49, 23, 58, 156, 31}, [{0,... \n","242 ({32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58,... \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 17 \n","1 25 \n","2 17 \n","3 16 \n","4 14 \n",".. ... \n","238 20 \n","239 24 \n","240 21 \n","241 35 \n","242 30 \n","\n"," Approximation and Heuristics Average Clustering \\\n","0 0.465 \n","1 0.563 \n","2 0.489 \n","3 0.461 \n","4 0.490 \n",".. ... \n","238 0.500 \n","239 0.531 \n","240 0.526 \n","241 0.623 \n","242 0.598 \n","\n"," Approximation and Heuristics Diameter \\\n","0 3 \n","1 3 \n","2 4 \n","3 3 \n","4 3 \n",".. ... \n","238 3 \n","239 3 \n","240 3 \n","241 3 \n","242 3 \n","\n"," Approximation and Heuristics Min Edge Dominating Set ... Chordal \\\n","0 {(54, 55), (86, 87), (125, 126), (17, 20), (40... ... False \n","1 {(125, 126), (26, 28), (17, 20), (72, 73), (35... ... False \n","2 {(54, 55), (86, 87), (125, 126), (40, 41), (72... ... False \n","3 {(134, 137), (65, 67), (54, 55), (30, 41), (15... ... False \n","4 {(54, 55), (86, 87), (156, 157), (40, 41), (72... ... False \n",".. ... ... ... \n","238 {(125, 126), (40, 41), (18, 19), (34, 35), (23... ... False \n","239 {(43, 48), (156, 157), (40, 41), (110, 111), (... ... False \n","240 {(86, 87), (33, 36), (72, 73), (141, 145), (18... ... False \n","241 {(62, 64), (125, 126), (156, 157), (18, 19), (... ... False \n","242 {(54, 55), (156, 157), (86, 90), (40, 41), (34... ... False \n","\n"," Maximal Cliques Num of isolates Non Randomness wrt Random Model \\\n","0 1813 0 -0.570663 \n","1 5810 0 10.101452 \n","2 3860 0 7.200119 \n","3 3505 0 7.945752 \n","4 3339 0 5.800827 \n",".. ... ... ... \n","238 4429 0 -4.078784 \n","239 3767 0 8.362277 \n","240 2133 0 7.042686 \n","241 102687 0 18.747141 \n","242 8572 0 16.102848 \n","\n"," Transitivity Connected Components Diameter 1 Edge Connected \\\n","0 0.503559 1 3 True \n","1 0.548962 1 3 True \n","2 0.492561 1 4 True \n","3 0.464850 1 3 True \n","4 0.472348 1 3 True \n",".. ... ... ... ... \n","238 0.498773 1 3 True \n","239 0.549560 1 3 True \n","240 0.499686 1 3 True \n","241 0.664289 1 3 True \n","242 0.620705 1 3 True \n","\n"," 2 Edge Connected 3 Edge Connected \n","0 True True \n","1 True True \n","2 False False \n","3 True True \n","4 True True \n",".. ... ... \n","238 True True \n","239 True True \n","240 True True \n","241 True True \n","242 True True \n","\n","[243 rows x 38 columns]"],"text/html":["\n","
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SubjectSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent SetsApproximation and Heuristics Max CliquesApproximation and Heuristics Clique RemovalApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average ClusteringApproximation and Heuristics DiameterApproximation and Heuristics Min Edge Dominating Set...ChordalMaximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge Connected
02001010{160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 14...{32, 33, 2, 38, 72, 73, 43, 140, 148, 149, 22,...({160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 1...170.4653{(54, 55), (86, 87), (125, 126), (17, 20), (40......False18130-0.5706630.50355913TrueTrueTrue
12002011{0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93, 94}{12, 14, 15, 145, 146, 17, 158, 34, 35, 36, 68...({0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93,...250.5633{(125, 126), (26, 28), (17, 20), (72, 73), (35......False5810010.1014520.54896213TrueTrueTrue
2200301{96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24,...{32, 34, 68, 36, 70, 40, 42, 107, 13, 111, 16,...({96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24...170.4894{(54, 55), (86, 87), (125, 126), (40, 41), (72......False386007.2001190.49256114TrueFalseFalse
32004010{4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61,...{64, 102, 103, 104, 46, 50, 51, 52, 54, 58, 29}({4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61...160.4613{(134, 137), (65, 67), (54, 55), (30, 41), (15......False350507.9457520.46485013TrueTrueTrue
42005015{0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 15...{128, 0, 131, 132, 133, 134, 136, 11, 83, 84, ...({0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 1...140.4903{(54, 55), (86, 87), (156, 157), (40, 41), (72......False333905.8008270.47234813TrueTrueTrue
..................................................................
2384156111{161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14...{160, 33, 32, 136, 8, 138, 139, 140, 146, 147,...({161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 1...200.5003{(125, 126), (40, 41), (18, 19), (34, 35), (23......False44290-4.0787840.49877313TrueTrueTrue
2394159112{160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 11...{132, 5, 6, 7, 4, 9, 34, 35, 45, 46, 64, 65, 7...({160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 1...240.5313{(43, 48), (156, 157), (40, 41), (110, 111), (......False376708.3622770.54956013TrueTrueTrue
240416915{130, 132, 133, 100, 137, 74, 42, 11, 141, 143...{64, 65, 4, 5, 6, 7, 9, 44, 45, 112, 81, 116, ...({130, 132, 133, 100, 137, 74, 42, 11, 141, 14...210.5263{(86, 87), (33, 36), (72, 73), (141, 145), (18......False213307.0426860.49968613TrueTrueTrue
241417016NaN{11, 12, 13, 14, 15, 144, 24, 27, 29, 32, 33, ...({161, 1, 4, 7, 16, 49, 23, 58, 156, 31}, [{0,...350.6233{(62, 64), (125, 126), (156, 157), (18, 19), (......False102687018.7471410.66428913TrueTrueTrue
242417118{32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58, ...{4, 133, 134, 7, 6, 9, 5, 145, 34, 35, 44, 45,...({32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58,...300.5983{(54, 55), (156, 157), (86, 90), (40, 41), (34......False8572016.1028480.62070513TrueTrueTrue
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243 rows × 38 columns

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SubjectAverage shortest pathStoer Wagner cutsWiener IndexDijkstra pathMax weight matchingConductanceRandomized Partitioning Heuristic
020010.00804219.841134107.483595882116.917205(1340.0942298403615, ({0, 3, 4, 5, 6, 12, 13, ...
120020.01213619.315941162.212200482126.843205(1491.6328930370037, ({1, 129, 130, 4, 5, 6, 7...
220030.01018216.432399136.090766382111.259694(1302.932983262392, ({1, 3, 5, 6, 7, 8, 12, 13...
320040.00946020.374916126.446053682119.750835(1283.965973913516, ({0, 1, 3, 4, 6, 8, 11, 13...
420050.01118220.140523149.462698782114.872774(1304.7065863045175, ({1, 2, 3, 4, 7, 8, 9, 10...
...........................
26141670.01165519.283984155.780433682NaN(1456.528461115162, ({1, 8, 9, 10, 12, 13, 15,...
26241680.01228020.846043164.140639782NaN(1459.219925223858, ({0, 1, 2, 4, 8, 10, 12, 1...
26341690.01193118.323694159.472844882NaN(1484.4315153492448, ({0, 1, 3, 4, 5, 8, 9, 12...
26441700.01346920.179314180.026202482NaN(1639.2320994076063, ({1, 2, 4, 5, 6, 7, 8, 9,...
26541710.01113420.074664148.814281682NaN(1550.9123617475766, ({129, 130, 131, 4, 5, 6,...
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265 rows × 8 columns

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\n"," "]},"metadata":{},"execution_count":5}]},{"cell_type":"code","source":["df = df.merge(df2, on='Subject', how='inner',)"],"metadata":{"id":"tFn3RocE0FD2"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# DATA CLEANING"],"metadata":{"id":"HeIxk4kqcjl2"}},{"cell_type":"code","source":["df = df.drop(['Approximation and Heuristics Clique Removal','Approximation and Heuristics Min Edge Dominating Set', 'Approximation and Heuristics Maximal Matching',\n"," 'Approximation and Heuristics Ramsay', 'Approximation and Heuristics treewidth Min Wt Vertex Cover','Conductance'], axis=1)\n","df"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":904},"id":"MOV4acpS1RNI","outputId":"d10856ff-66f5-4d31-d263-06d262ad3728","executionInfo":{"status":"ok","timestamp":1671363796337,"user_tz":-330,"elapsed":15,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Average shortest path Stoer Wagner cuts Wiener Index \\\n","0 2001 0.008042 19.841134 107.483595 \n","1 2002 0.012136 19.315941 162.212200 \n","2 2003 0.010182 16.432399 136.090766 \n","3 2004 0.009460 20.374916 126.446053 \n","4 2005 0.011182 20.140523 149.462698 \n",".. ... ... ... ... \n","238 4156 0.010345 21.208409 138.275598 \n","239 4159 0.010946 21.128360 146.306992 \n","240 4169 0.011931 18.323694 159.472844 \n","241 4170 0.013469 20.179314 180.026202 \n","242 4171 0.011134 20.074664 148.814281 \n","\n"," Dijkstra path Max weight matching \\\n","0 8 82 \n","1 4 82 \n","2 3 82 \n","3 6 82 \n","4 7 82 \n",".. ... ... \n","238 4 82 \n","239 9 82 \n","240 8 82 \n","241 4 82 \n","242 6 82 \n","\n"," Randomized Partitioning Heuristic Schizophrenic \\\n","0 (1340.0942298403615, ({0, 3, 4, 5, 6, 12, 13, ... 0 \n","1 (1491.6328930370037, ({1, 129, 130, 4, 5, 6, 7... 0 \n","2 (1302.932983262392, ({1, 3, 5, 6, 7, 8, 12, 13... 0 \n","3 (1283.965973913516, ({0, 1, 3, 4, 6, 8, 11, 13... 0 \n","4 (1304.7065863045175, ({1, 2, 3, 4, 7, 8, 9, 10... 0 \n",".. ... ... \n","238 (1426.8818395540534, ({0, 3, 4, 7, 9, 10, 12, ... 1 \n","239 (1494.8627601239193, ({0, 1, 4, 5, 7, 10, 15, ... 1 \n","240 (1484.4315153492448, ({0, 1, 3, 4, 5, 8, 9, 12... 1 \n","241 (1639.2320994076063, ({1, 2, 4, 5, 6, 7, 8, 9,... 1 \n","242 (1550.9123617475766, ({129, 130, 131, 4, 5, 6,... 1 \n","\n"," Approximation and Heuristics Node Connectivity \\\n","0 10 \n","1 11 \n","2 1 \n","3 10 \n","4 15 \n",".. ... \n","238 11 \n","239 12 \n","240 5 \n","241 6 \n","242 8 \n","\n"," Approximation and Heuristics Max Independent Sets ... Chordal \\\n","0 {160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 14... ... False \n","1 {0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93, 94} ... False \n","2 {96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24,... ... False \n","3 {4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61,... ... False \n","4 {0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 15... ... False \n",".. ... ... ... \n","238 {161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14... ... False \n","239 {160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 11... ... False \n","240 {130, 132, 133, 100, 137, 74, 42, 11, 141, 143... ... False \n","241 NaN ... False \n","242 {32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58, ... ... False \n","\n"," Maximal Cliques Num of isolates Non Randomness wrt Random Model \\\n","0 1813 0 -0.570663 \n","1 5810 0 10.101452 \n","2 3860 0 7.200119 \n","3 3505 0 7.945752 \n","4 3339 0 5.800827 \n",".. ... ... ... \n","238 4429 0 -4.078784 \n","239 3767 0 8.362277 \n","240 2133 0 7.042686 \n","241 102687 0 18.747141 \n","242 8572 0 16.102848 \n","\n"," Transitivity Connected Components Diameter 1 Edge Connected \\\n","0 0.503559 1 3 True \n","1 0.548962 1 3 True \n","2 0.492561 1 4 True \n","3 0.464850 1 3 True \n","4 0.472348 1 3 True \n",".. ... ... ... ... \n","238 0.498773 1 3 True \n","239 0.549560 1 3 True \n","240 0.499686 1 3 True \n","241 0.664289 1 3 True \n","242 0.620705 1 3 True \n","\n"," 2 Edge Connected 3 Edge Connected \n","0 True True \n","1 True True \n","2 False False \n","3 True True \n","4 True True \n",".. ... ... \n","238 True True \n","239 True True \n","240 True True \n","241 True True \n","242 True True \n","\n","[243 rows x 39 columns]"],"text/html":["\n","
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SubjectAverage shortest pathStoer Wagner cutsWiener IndexDijkstra pathMax weight matchingRandomized Partitioning HeuristicSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Max Independent Sets...ChordalMaximal CliquesNum of isolatesNon Randomness wrt Random ModelTransitivityConnected ComponentsDiameter1 Edge Connected2 Edge Connected3 Edge Connected
020010.00804219.841134107.483595882(1340.0942298403615, ({0, 3, 4, 5, 6, 12, 13, ...010{160, 129, 2, 3, 0, 6, 7, 11, 108, 142, 46, 14......False18130-0.5706630.50355913TrueTrueTrue
120020.01213619.315941162.212200482(1491.6328930370037, ({1, 129, 130, 4, 5, 6, 7...011{0, 129, 1, 8, 10, 12, 141, 143, 18, 152, 93, 94}...False5810010.1014520.54896213TrueTrueTrue
220030.01018216.432399136.090766382(1302.932983262392, ({1, 3, 5, 6, 7, 8, 12, 13...01{96, 1, 0, 5, 8, 137, 11, 141, 46, 49, 87, 24,......False386007.2001190.49256114TrueFalseFalse
320040.00946020.374916126.446053682(1283.965973913516, ({0, 1, 3, 4, 6, 8, 11, 13...010{4, 39, 8, 7, 74, 13, 51, 148, 20, 19, 27, 61,......False350507.9457520.46485013TrueTrueTrue
420050.01118220.140523149.462698782(1304.7065863045175, ({1, 2, 3, 4, 7, 8, 9, 10...015{0, 129, 1, 99, 4, 6, 7, 41, 138, 108, 150, 15......False333905.8008270.47234813TrueTrueTrue
..................................................................
23841560.01034521.208409138.275598482(1426.8818395540534, ({0, 3, 4, 7, 9, 10, 12, ...111{161, 65, 2, 132, 100, 58, 36, 11, 109, 78, 14......False44290-4.0787840.49877313TrueTrueTrue
23941590.01094621.128360146.306992982(1494.8627601239193, ({0, 1, 4, 5, 7, 10, 15, ...112{160, 1, 163, 100, 133, 36, 26, 10, 12, 19, 11......False376708.3622770.54956013TrueTrueTrue
24041690.01193118.323694159.472844882(1484.4315153492448, ({0, 1, 3, 4, 5, 8, 9, 12...15{130, 132, 133, 100, 137, 74, 42, 11, 141, 143......False213307.0426860.49968613TrueTrueTrue
24141700.01346920.179314180.026202482(1639.2320994076063, ({1, 2, 4, 5, 6, 7, 8, 9,...16NaN...False102687018.7471410.66428913TrueTrueTrue
24241710.01113420.074664148.814281682(1550.9123617475766, ({129, 130, 131, 4, 5, 6,...18{32, 1, 26, 8, 11, 143, 79, 61, 119, 153, 58, ......False8572016.1028480.62070513TrueTrueTrue
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243 rows × 39 columns

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\n"," "]},"metadata":{},"execution_count":7}]},{"cell_type":"code","source":["df['Approximation and Heuristics Max Independent Sets'] = len(df['Approximation and Heuristics Max Independent Sets'])\n","df['Asteroidal Triple']= len(df['Asteroidal Triple'])\n","df['Approximation and Heuristics Max Cliques'] = len(df['Approximation and Heuristics Max Cliques'])\n","df['Approximation and Heuristics TSP'] = len(df['Approximation and Heuristics TSP'])\n","df['Approximation and Heuristics Diameter'] = len(df['Approximation and Heuristics Diameter'])\n","df['Approximation and Heuristics Min Wt Dominating Set'] = len(df['Approximation and Heuristics Min Wt Dominating Set'])\n","df['Approximation and Heuristics Randomized Partitioning'] = df['Approximation and Heuristics Randomized Partitioning'].apply(lambda k: eval(k)).apply(lambda k: k[0])\n","df['Approximation and Heuristics One Exchange'] = df['Approximation and Heuristics One Exchange'].apply(lambda k: eval(k)).apply(lambda k: k[0])"],"metadata":{"id":"JDCinmtSckxC"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df['1 Edge Connected'] = df['1 Edge Connected'].map({True:1 ,False:0})\n","df['2 Edge Connected'] = df['2 Edge Connected'].map({True:1 ,False:0})\n","df['3 Edge Connected'] = df['3 Edge Connected'].map({True:1 ,False:0})\n","df['Bridges'] = df['Bridges'].map({True:1 ,False:0})\n","df['Chordal'] = df['Chordal'].map({True:1 ,False:0})"],"metadata":{"id":"GV8zw0ua2P3z"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df['Randomized Partitioning Heuristic'] = df['Randomized Partitioning Heuristic'].apply(lambda k: eval(k))\n","df['Randomized Partitioning Heuristic'] = df['Randomized Partitioning Heuristic'].apply(lambda k: k[0])"],"metadata":{"id":"ksK6jjz03o36"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["non_unique=list()\n","for column in df:\n"," if(len(pd.unique(df[column]))==1):\n"," non_unique.append(column)\n","\n","non_unique"],"metadata":{"id":"YoqXadJFBrFX","colab":{"base_uri":"https://localhost:8080/"},"outputId":"e223ab8e-237e-4ba6-9079-8b2edae384ff","executionInfo":{"status":"ok","timestamp":1671363796338,"user_tz":-330,"elapsed":15,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["['Max weight matching',\n"," 'Approximation and Heuristics Max Independent Sets',\n"," 'Approximation and Heuristics Max Cliques',\n"," 'Approximation and Heuristics Diameter',\n"," 'Approximation and Heuristics Min Wt Dominating Set',\n"," 'Approximation and Heuristics TSP',\n"," 'Asteroidal Triple',\n"," 'Chordal',\n"," 'Num of isolates',\n"," 'Connected Components',\n"," '1 Edge Connected']"]},"metadata":{},"execution_count":11}]},{"cell_type":"code","source":["df=df.drop(non_unique, axis=1)"],"metadata":{"id":"yX3kis6iBzxW"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df = df.fillna(0)"],"metadata":{"id":"ywa1ben3NksL"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":557},"id":"is8ZQYn-NqkN","outputId":"84f0d857-a7ac-43bb-efcb-1497a52b56e6","executionInfo":{"status":"ok","timestamp":1671363796338,"user_tz":-330,"elapsed":13,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Average shortest path Stoer Wagner cuts Wiener Index \\\n","0 2001 0.008042 19.841134 107.483595 \n","1 2002 0.012136 19.315941 162.212200 \n","2 2003 0.010182 16.432399 136.090766 \n","3 2004 0.009460 20.374916 126.446053 \n","4 2005 0.011182 20.140523 149.462698 \n",".. ... ... ... ... \n","238 4156 0.010345 21.208409 138.275598 \n","239 4159 0.010946 21.128360 146.306992 \n","240 4169 0.011931 18.323694 159.472844 \n","241 4170 0.013469 20.179314 180.026202 \n","242 4171 0.011134 20.074664 148.814281 \n","\n"," Dijkstra path Randomized Partitioning Heuristic Schizophrenic \\\n","0 8 1340.094230 0 \n","1 4 1491.632893 0 \n","2 3 1302.932983 0 \n","3 6 1283.965974 0 \n","4 7 1304.706586 0 \n",".. ... ... ... \n","238 4 1426.881840 1 \n","239 9 1494.862760 1 \n","240 8 1484.431515 1 \n","241 4 1639.232099 1 \n","242 6 1550.912362 1 \n","\n"," Approximation and Heuristics Node Connectivity \\\n","0 10 \n","1 11 \n","2 1 \n","3 10 \n","4 15 \n",".. ... \n","238 11 \n","239 12 \n","240 5 \n","241 6 \n","242 8 \n","\n"," Approximation and Heuristics Large Clique Size \\\n","0 17 \n","1 25 \n","2 17 \n","3 16 \n","4 14 \n",".. ... \n","238 20 \n","239 24 \n","240 21 \n","241 35 \n","242 30 \n","\n"," Approximation and Heuristics Average Clustering ... Graph colouring \\\n","0 0.465 ... 19 \n","1 0.563 ... 31 \n","2 0.489 ... 22 \n","3 0.461 ... 19 \n","4 0.490 ... 19 \n",".. ... ... ... \n","238 0.500 ... 23 \n","239 0.531 ... 30 \n","240 0.526 ... 24 \n","241 0.623 ... 41 \n","242 0.598 ... 33 \n","\n"," Avg Degree Global Clustering Edges Maximal Cliques \\\n","0 17.512195 0.492320 2872 1813 \n","1 24.396341 0.541610 4001 5810 \n","2 20.628049 0.499233 3383 3860 \n","3 19.115854 0.462352 3135 3505 \n","4 19.762195 0.477082 3241 3339 \n",".. ... ... ... ... \n","238 20.682927 0.497645 3392 4429 \n","239 23.012195 0.551732 3774 3767 \n","240 18.987805 0.485025 3114 2133 \n","241 34.280488 0.632228 5622 102687 \n","242 26.432927 0.594931 4335 8572 \n","\n"," Non Randomness wrt Random Model Transitivity Diameter \\\n","0 -0.570663 0.503559 3 \n","1 10.101452 0.548962 3 \n","2 7.200119 0.492561 4 \n","3 7.945752 0.464850 3 \n","4 5.800827 0.472348 3 \n",".. ... ... ... \n","238 -4.078784 0.498773 3 \n","239 8.362277 0.549560 3 \n","240 7.042686 0.499686 3 \n","241 18.747141 0.664289 3 \n","242 16.102848 0.620705 3 \n","\n"," 2 Edge Connected 3 Edge Connected \n","0 1 1 \n","1 1 1 \n","2 0 0 \n","3 1 1 \n","4 1 1 \n",".. ... ... \n","238 1 1 \n","239 1 1 \n","240 1 1 \n","241 1 1 \n","242 1 1 \n","\n","[243 rows x 28 columns]"],"text/html":["\n","
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SubjectAverage shortest pathStoer Wagner cutsWiener IndexDijkstra pathRandomized Partitioning HeuristicSchizophrenicApproximation and Heuristics Node ConnectivityApproximation and Heuristics Large Clique SizeApproximation and Heuristics Average Clustering...Graph colouringAvg DegreeGlobal ClusteringEdgesMaximal CliquesNon Randomness wrt Random ModelTransitivityDiameter2 Edge Connected3 Edge Connected
020010.00804219.841134107.48359581340.094230010170.465...1917.5121950.49232028721813-0.5706630.503559311
120020.01213619.315941162.21220041491.632893011250.563...3124.3963410.5416104001581010.1014520.548962311
220030.01018216.432399136.09076631302.93298301170.489...2220.6280490.499233338338607.2001190.492561400
320040.00946020.374916126.44605361283.965974010160.461...1919.1158540.462352313535057.9457520.464850311
420050.01118220.140523149.46269871304.706586015140.490...1919.7621950.477082324133395.8008270.472348311
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23841560.01034521.208409138.27559841426.881840111200.500...2320.6829270.49764533924429-4.0787840.498773311
23941590.01094621.128360146.30699291494.862760112240.531...3023.0121950.551732377437678.3622770.549560311
24041690.01193118.323694159.47284481484.43151515210.526...2418.9878050.485025311421337.0426860.499686311
24141700.01346920.179314180.02620241639.23209916350.623...4134.2804880.632228562210268718.7471410.664289311
24241710.01113420.074664148.81428161550.91236218300.598...3326.4329270.5949314335857216.1028480.620705311
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243 rows × 28 columns

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\n"," "]},"metadata":{},"execution_count":14}]},{"cell_type":"code","source":["df.info()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"9AnLjNxQ2Qiw","outputId":"e0ba7559-2108-4349-9cfc-8ae9d79efacb","executionInfo":{"status":"ok","timestamp":1671363796338,"user_tz":-330,"elapsed":13,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["\n","Int64Index: 243 entries, 0 to 242\n","Data columns (total 28 columns):\n"," # Column Non-Null Count Dtype \n","--- ------ -------------- ----- \n"," 0 Subject 243 non-null int64 \n"," 1 Average shortest path 243 non-null float64\n"," 2 Stoer Wagner cuts 243 non-null float64\n"," 3 Wiener Index 243 non-null float64\n"," 4 Dijkstra path 243 non-null int64 \n"," 5 Randomized Partitioning Heuristic 243 non-null float64\n"," 6 Schizophrenic 243 non-null int64 \n"," 7 Approximation and Heuristics Node Connectivity 243 non-null int64 \n"," 8 Approximation and Heuristics Large Clique Size 243 non-null int64 \n"," 9 Approximation and Heuristics Average Clustering 243 non-null float64\n"," 10 Approximation and Heuristics treewidth Min Degree 243 non-null int64 \n"," 11 Approximation and Heuristics treewidth Min Fill In 243 non-null int64 \n"," 12 Approximation and Heuristics Randomized Partitioning 243 non-null int64 \n"," 13 Approximation and Heuristics One Exchange 243 non-null int64 \n"," 14 Degree Assortativity 243 non-null float64\n"," 15 Avg Shortest Path Length 243 non-null float64\n"," 16 Bridges 243 non-null int64 \n"," 17 Local Bridges 243 non-null int64 \n"," 18 Graph colouring 243 non-null int64 \n"," 19 Avg Degree 243 non-null float64\n"," 20 Global Clustering 243 non-null float64\n"," 21 Edges 243 non-null int64 \n"," 22 Maximal Cliques 243 non-null int64 \n"," 23 Non Randomness wrt Random Model 243 non-null float64\n"," 24 Transitivity 243 non-null float64\n"," 25 Diameter 243 non-null int64 \n"," 26 2 Edge Connected 243 non-null int64 \n"," 27 3 Edge Connected 243 non-null int64 \n","dtypes: float64(11), int64(17)\n","memory usage: 55.1 KB\n"]}]},{"cell_type":"code","source":["dfs = [df]"],"metadata":{"id":"Dqhxxfif2ZrC"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# TEST TRAIN SPLIT"],"metadata":{"id":"RkgR-AHifmHo"}},{"cell_type":"code","source":["def preprocessing_pipeline(X):\n"," return X"],"metadata":{"id":"Q27iuywrkQhI"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["def split_fn(df):\n"," X = df.drop(['Schizophrenic','Subject'], axis=1)\n"," y = df['Schizophrenic']\n","\n"," return X, y"],"metadata":{"id":"eWtyaiVcfnS6"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["def main(df, clf, param):\n"," # data\n"," X, y = split_fn(df)\n"," X = preprocessing_pipeline(X)\n","\n"," # grid\n"," gscv = GridSearchCV(clf, param, cv=10, scoring='accuracy' )\n"," gscv.fit(X, y)\n","\n"," print(gscv.get_params())\n","\n"," return gscv"],"metadata":{"id":"weeq2BAXqKcZ"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["#ML Models "],"metadata":{"id":"9qfA5N6gNdxo"}},{"cell_type":"markdown","source":["## LR"],"metadata":{"id":"EdejbCntfoU3"}},{"cell_type":"code","source":["clf = LogisticRegression()"],"metadata":{"id":"_QWpgLXXfqFD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["dt = clf\n","X, y = split_fn(df)\n","acc = []\n","f1 = []\n","recall = []\n","prec = []\n","spec = []\n","for r in range(1,11):\n"," X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state = r)\n"," dt.fit(X_train, y_train)\n"," pred = dt.predict(X_test)\n"," acc.append(accuracy_score(y_test, pred))\n"," f1.append(f1_score(y_test, pred))\n"," recall.append(recall_score(y_test, pred))\n"," prec.append(precision_score(y_test, pred))\n"," tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()\n"," specificity = tn / (tn+fp)\n"," spec.append(specificity)\n"," \n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average specificity: %.3f +/- %.3f' %(np.mean(spec), np.std(spec)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(recall), np.std(recall)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(prec), np.std(prec)))\n","print('Average f1: %.3f +/- %.3f' %(np.mean(f1), np.std(f1)))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"oo_gpyHYfs5s","outputId":"b6589092-d7aa-4eab-aeb2-88241a500680","executionInfo":{"status":"ok","timestamp":1671363863522,"user_tz":-330,"elapsed":641,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Average accccuracy: 0.612 +/- 0.069\n","Average specificity: 0.667 +/- 0.118\n","Average recall: 0.564 +/- 0.076\n","Average precision: 0.606 +/- 0.141\n","Average f1: 0.577 +/- 0.086\n"]}]},{"cell_type":"markdown","source":["## SVM"],"metadata":{"id":"fAx2U4HbWqdX"}},{"cell_type":"code","source":["clf = SVC()\n","parameters = {'C': [0.1, 1, 10, 100,1000], \n"," 'gamma': [1, 0.1, 0.01, 0.001,0.0001],\n"," 'kernel': ['rbf']} "],"metadata":{"id":"j-0er4AjWsZ7"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["res = []\n","for df in dfs: \n"," res.append(main(df, clf, parameters))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"mgdtLTkzYAXB","outputId":"edef9889-5305-4247-bf34-afedd2f87323","executionInfo":{"status":"ok","timestamp":1671363865679,"user_tz":-330,"elapsed":2159,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["{'cv': 10, 'error_score': nan, 'estimator__C': 1.0, 'estimator__break_ties': False, 'estimator__cache_size': 200, 'estimator__class_weight': None, 'estimator__coef0': 0.0, 'estimator__decision_function_shape': 'ovr', 'estimator__degree': 3, 'estimator__gamma': 'scale', 'estimator__kernel': 'rbf', 'estimator__max_iter': -1, 'estimator__probability': False, 'estimator__random_state': None, 'estimator__shrinking': True, 'estimator__tol': 0.001, 'estimator__verbose': False, 'estimator': SVC(), 'n_jobs': None, 'param_grid': {'C': [0.1, 1, 10, 100, 1000], 'gamma': [1, 0.1, 0.01, 0.001, 0.0001], 'kernel': ['rbf']}, 'pre_dispatch': '2*n_jobs', 'refit': True, 'return_train_score': False, 'scoring': 'accuracy', 'verbose': 0}\n"]}]},{"cell_type":"code","source":["for clf in res:\n"," print(clf.best_estimator_, clf.best_params_, clf.best_score_)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"XxP0dI_7YB0t","outputId":"45af0372-d2e2-4441-c242-9f0a2e80970d","executionInfo":{"status":"ok","timestamp":1671363865680,"user_tz":-330,"elapsed":8,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["SVC(C=1, gamma=0.0001) {'C': 1, 'gamma': 0.0001, 'kernel': 'rbf'} 0.8053333333333332\n"]}]},{"cell_type":"code","source":["dt = clf.best_estimator_"],"metadata":{"id":"WFc_a92nT7Mf"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["X, y = split_fn(df)\n","acc = []\n","f1 = []\n","recall = []\n","prec = []\n","spec = []\n","for r in range(1,11):\n"," X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state = r)\n"," dt.fit(X_train, y_train)\n"," pred = dt.predict(X_test)\n"," acc.append(accuracy_score(y_test, pred))\n"," f1.append(f1_score(y_test, pred))\n"," recall.append(recall_score(y_test, pred))\n"," prec.append(precision_score(y_test, pred))\n"," tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()\n"," specificity = tn / (tn+fp)\n"," spec.append(specificity)\n"," \n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average specificity: %.3f +/- %.3f' %(np.mean(spec), np.std(spec)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(recall), np.std(recall)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(prec), np.std(prec)))\n","print('Average f1: %.3f +/- %.3f' %(np.mean(f1), np.std(f1)))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Pbc3pr_RYEbW","outputId":"74acd5fa-ffca-465e-fb8d-22c1c3716721","executionInfo":{"status":"ok","timestamp":1671363865680,"user_tz":-330,"elapsed":5,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Average accccuracy: 0.790 +/- 0.051\n","Average specificity: 0.900 +/- 0.052\n","Average recall: 0.676 +/- 0.105\n","Average precision: 0.852 +/- 0.076\n","Average f1: 0.747 +/- 0.074\n"]}]},{"cell_type":"markdown","source":["## KNN"],"metadata":{"id":"cCHKKJdFTbzg"}},{"cell_type":"code","source":["clf = KNeighborsClassifier()\n","parameters = {'n_neighbors': list(range(3,50)),\n"," # 'weights': ['uniform','distance', None],\n"," 'p': [1,2]\n"," }"],"metadata":{"id":"NGEB-AC-TbIx"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["res = []\n","for df in dfs: \n"," res.append(main(df, clf, parameters))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"vfvwoQ1mTuFR","outputId":"2da2209f-38b4-4916-82e6-5d40656d8561","executionInfo":{"status":"ok","timestamp":1671363871518,"user_tz":-330,"elapsed":5842,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["{'cv': 10, 'error_score': nan, 'estimator__algorithm': 'auto', 'estimator__leaf_size': 30, 'estimator__metric': 'minkowski', 'estimator__metric_params': None, 'estimator__n_jobs': None, 'estimator__n_neighbors': 5, 'estimator__p': 2, 'estimator__weights': 'uniform', 'estimator': KNeighborsClassifier(), 'n_jobs': None, 'param_grid': {'n_neighbors': [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], 'p': [1, 2]}, 'pre_dispatch': '2*n_jobs', 'refit': True, 'return_train_score': False, 'scoring': 'accuracy', 'verbose': 0}\n"]}]},{"cell_type":"code","source":["for clf in res:\n"," print(clf.best_estimator_, clf.best_params_, clf.best_score_)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nBfqUxFmT1YA","outputId":"894344bb-8f90-420d-b017-04d3202a4369","executionInfo":{"status":"ok","timestamp":1671363871518,"user_tz":-330,"elapsed":12,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["KNeighborsClassifier(n_neighbors=3, p=1) {'n_neighbors': 3, 'p': 1} 0.7241666666666666\n"]}]},{"cell_type":"markdown","source":["### 10 fold cv"],"metadata":{"id":"IzpjlFvUVgma"}},{"cell_type":"code","source":["dt = clf.best_estimator_"],"metadata":{"id":"4uualR7BT5kM"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["X, y = split_fn(df)\n","acc = []\n","f1 = []\n","recall = []\n","prec = []\n","spec = []\n","for r in range(1,11):\n"," X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state = r)\n"," dt.fit(X_train, y_train)\n"," pred = dt.predict(X_test)\n"," acc.append(accuracy_score(y_test, pred))\n"," f1.append(f1_score(y_test, pred))\n"," recall.append(recall_score(y_test, pred))\n"," prec.append(precision_score(y_test, pred))\n"," tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()\n"," specificity = tn / (tn+fp)\n"," spec.append(specificity)\n"," \n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average specificity: %.3f +/- %.3f' %(np.mean(spec), np.std(spec)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(recall), np.std(recall)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(prec), np.std(prec)))\n","print('Average f1: %.3f +/- %.3f' %(np.mean(f1), np.std(f1)))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"LqrLxkoKVh8h","outputId":"33b084e8-32e5-4493-b6e3-20f64a8c80f7","executionInfo":{"status":"ok","timestamp":1671363871519,"user_tz":-330,"elapsed":11,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Average accccuracy: 0.682 +/- 0.086\n","Average specificity: 0.640 +/- 0.117\n","Average recall: 0.732 +/- 0.089\n","Average precision: 0.647 +/- 0.113\n","Average f1: 0.683 +/- 0.090\n"]}]},{"cell_type":"markdown","source":["## Decision Tree"],"metadata":{"id":"yM7PZDfTNfRR"}},{"cell_type":"code","source":["dt = DecisionTreeClassifier()\n","parameters = {'criterion': ['gini', 'entropy'],\n"," 'max_depth': list(range(1,50,2)),\n"," }"],"metadata":{"id":"3yfe46JfRdCX"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["res = []\n","for df in dfs: \n"," res.append(main(df, dt, parameters))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"outputId":"8db7d64a-c479-4f7d-81a6-07395e0c320e","id":"8ahk1lsERdCX","executionInfo":{"status":"ok","timestamp":1671363874762,"user_tz":-330,"elapsed":3253,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["{'cv': 10, 'error_score': nan, 'estimator__ccp_alpha': 0.0, 'estimator__class_weight': None, 'estimator__criterion': 'gini', 'estimator__max_depth': None, 'estimator__max_features': None, 'estimator__max_leaf_nodes': None, 'estimator__min_impurity_decrease': 0.0, 'estimator__min_samples_leaf': 1, 'estimator__min_samples_split': 2, 'estimator__min_weight_fraction_leaf': 0.0, 'estimator__random_state': None, 'estimator__splitter': 'best', 'estimator': DecisionTreeClassifier(), 'n_jobs': None, 'param_grid': {'criterion': ['gini', 'entropy'], 'max_depth': [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]}, 'pre_dispatch': '2*n_jobs', 'refit': True, 'return_train_score': False, 'scoring': 'accuracy', 'verbose': 0}\n"]}]},{"cell_type":"code","source":["for clf in res:\n"," print(clf.best_estimator_, clf.best_params_, clf.best_score_)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"_68RoBtXRbVM","outputId":"019da219-5d4a-4e9c-edb3-ef9d9e1bbc00","executionInfo":{"status":"ok","timestamp":1671363874762,"user_tz":-330,"elapsed":11,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["DecisionTreeClassifier(max_depth=15) {'criterion': 'gini', 'max_depth': 15} 0.8276666666666668\n"]}]},{"cell_type":"markdown","source":["### 10 fold CV"],"metadata":{"id":"EuRtQ51TQVA5"}},{"cell_type":"code","source":["dt = clf.best_estimator_"],"metadata":{"id":"X7Pl1rnBTl5F"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["X, y = split_fn(df)\n","acc = []\n","f1 = []\n","recall = []\n","prec = []\n","spec = []\n","for r in range(21,31):\n"," X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state = r)\n"," dt.fit(X_train, y_train)\n"," pred = dt.predict(X_test)\n"," acc.append(accuracy_score(y_test, pred))\n"," f1.append(f1_score(y_test, pred))\n"," recall.append(recall_score(y_test, pred))\n"," prec.append(precision_score(y_test, pred))\n"," tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()\n"," specificity = tn / (tn+fp)\n"," spec.append(specificity)\n"," \n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average specificity: %.3f +/- %.3f' %(np.mean(spec), np.std(spec)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(recall), np.std(recall)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(prec), np.std(prec)))\n","print('Average f1: %.3f +/- %.3f' %(np.mean(f1), np.std(f1)))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"4OcbMdmkQXMd","outputId":"b24b5095-e7e4-47ed-bbf7-16697096c3ac","executionInfo":{"status":"ok","timestamp":1671363874763,"user_tz":-330,"elapsed":8,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Average accccuracy: 0.765 +/- 0.053\n","Average specificity: 0.701 +/- 0.071\n","Average recall: 0.828 +/- 0.052\n","Average precision: 0.734 +/- 0.079\n","Average f1: 0.776 +/- 0.060\n"]}]},{"cell_type":"markdown","source":["## AdaBoost"],"metadata":{"id":"niqltGWuQWn2"}},{"cell_type":"code","source":["clf = AdaBoostClassifier()\n","parameters = {'n_estimators': list(range(3,101,10)),\n"," 'learning_rate':[0.1,0.3,0.5,0.7,1.0],\n"," }"],"metadata":{"id":"HQnPSSp8r_eT"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["res = []\n","for df in dfs: \n"," res.append(main(df, clf, parameters))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"cwnojbHCv2sK","outputId":"062f0d8b-7a84-4ebb-a0ba-31c95c34fe74","executionInfo":{"status":"ok","timestamp":1671363923792,"user_tz":-330,"elapsed":49035,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["{'cv': 10, 'error_score': nan, 'estimator__algorithm': 'SAMME.R', 'estimator__base_estimator': None, 'estimator__learning_rate': 1.0, 'estimator__n_estimators': 50, 'estimator__random_state': None, 'estimator': AdaBoostClassifier(), 'n_jobs': None, 'param_grid': {'n_estimators': [3, 13, 23, 33, 43, 53, 63, 73, 83, 93], 'learning_rate': [0.1, 0.3, 0.5, 0.7, 1.0]}, 'pre_dispatch': '2*n_jobs', 'refit': True, 'return_train_score': False, 'scoring': 'accuracy', 'verbose': 0}\n"]}]},{"cell_type":"code","source":["for clf in res:\n"," print(clf.best_estimator_, clf.best_params_, clf.best_score_)"],"metadata":{"id":"VWwCP9HsBN07","colab":{"base_uri":"https://localhost:8080/"},"outputId":"11c2408c-7689-45b1-a8f0-d37391567785","executionInfo":{"status":"ok","timestamp":1671363923792,"user_tz":-330,"elapsed":4,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["AdaBoostClassifier(n_estimators=93) {'learning_rate': 1.0, 'n_estimators': 93} 0.7783333333333333\n"]}]},{"cell_type":"markdown","source":["### 10 fold CV"],"metadata":{"id":"uoVmo-76O4Xt"}},{"cell_type":"code","source":["dt = clf.best_estimator_"],"metadata":{"id":"vUc0ECN5Toww"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["X, y = split_fn(df)\n","acc = []\n","f1 = []\n","recall = []\n","prec = []\n","spec = []\n","for r in list(range(1,11)):\n"," X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state = r)\n"," clf.fit(X_train, y_train)\n"," pred = clf.predict(X_test)\n"," acc.append(accuracy_score(y_test, pred))\n"," f1.append(f1_score(y_test, pred))\n"," recall.append(recall_score(y_test, pred))\n"," prec.append(precision_score(y_test, pred))\n"," tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()\n"," specificity = tn / (tn+fp)\n"," spec.append(specificity)\n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average specificity: %.3f +/- %.3f' %(np.mean(spec), np.std(spec)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(recall), np.std(recall)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(prec), np.std(prec)))\n","print('Average f1: %.3f +/- %.3f' %(np.mean(f1), np.std(f1)))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Gs0OOGAe_fZK","outputId":"d7328c67-fe58-43f8-d156-b5a4b163528f","executionInfo":{"status":"ok","timestamp":1671364386111,"user_tz":-330,"elapsed":462321,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Average accccuracy: 0.755 +/- 0.062\n","Average specificity: 0.721 +/- 0.109\n","Average recall: 0.807 +/- 0.086\n","Average precision: 0.721 +/- 0.103\n","Average f1: 0.755 +/- 0.061\n"]}]}]} \ No newline at end of file diff --git a/Code/5. Graph Neural Network/DGCNN model 10 Fold CV.ipynb b/Code/5. Graph Neural Network/DGCNN model 10 Fold CV.ipynb new file mode 100644 index 0000000..ea69a02 --- /dev/null +++ b/Code/5. Graph Neural Network/DGCNN model 10 Fold CV.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"ZO0efz7FKcNH","outputId":"5928978d-dcfc-452c-ef92-fe06df1701a0","executionInfo":{"status":"ok","timestamp":1671424007979,"user_tz":-330,"elapsed":27139,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"34Sj6CEbxsHH","outputId":"5e08df0c-b7f9-4a58-bc2b-00bad5e66c06"},"outputs":[{"output_type":"stream","name":"stdout","text":["Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Collecting stellargraph\n"," Downloading stellargraph-1.2.1-py3-none-any.whl (435 kB)\n","\u001b[K |████████████████████████████████| 435 kB 6.1 MB/s \n","\u001b[?25hRequirement already satisfied: tensorflow>=2.1.0 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (2.9.2)\n","Requirement already satisfied: matplotlib>=2.2 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (3.2.2)\n","Requirement already satisfied: networkx>=2.2 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (2.6.3)\n","Requirement already satisfied: gensim>=3.4.0 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (3.6.0)\n","Requirement already satisfied: scikit-learn>=0.20 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.0.2)\n","Requirement already satisfied: pandas>=0.24 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.3.5)\n","Requirement already satisfied: numpy>=1.14 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.21.6)\n","Requirement already satisfied: scipy>=1.1.0 in 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requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (3.2.2)\n","Installing collected packages: stellargraph\n","Successfully installed stellargraph-1.2.1\n","Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Requirement already satisfied: pyyaml in /usr/local/lib/python3.8/dist-packages (6.0)\n","Requirement already satisfied: h5py in /usr/local/lib/python3.8/dist-packages (3.1.0)\n","Requirement already satisfied: numpy>=1.17.5 in /usr/local/lib/python3.8/dist-packages (from h5py) (1.21.6)\n"]}],"source":["#installs\n","\n","!pip install stellargraph\n","!pip install pyyaml h5py"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OrtnMu3bNDm4"},"outputs":[],"source":["#imports \n","\n","from stellargraph import StellarGraph\n","import stellargraph as sg\n","from stellargraph.mapper import PaddedGraphGenerator\n","from stellargraph.layer import GCNSupervisedGraphClassification, DeepGraphCNN\n","import pandas as pd\n","import os\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","from sklearn.preprocessing import StandardScaler\n","from sklearn import model_selection\n","from IPython.display import display, HTML\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import math\n","from tensorflow.keras import Model\n","from tensorflow.keras.optimizers import Adam, SGD\n","from tensorflow.keras.layers import Dense, Conv1D, MaxPool1D, Dropout, Flatten\n","from tensorflow.keras.callbacks import EarlyStopping\n","from tensorflow.keras.layers import Dense\n","from tensorflow.keras.losses import binary_crossentropy\n","import tensorflow as tf\n","from sklearn import metrics\n","from tensorflow import keras\n","from sklearn.metrics import f1_score, precision_score, confusion_matrix, classification_report, confusion_matrix, ConfusionMatrixDisplay, roc_auc_score\n","import warnings\n","warnings.filterwarnings(\"ignore\")"]},{"cell_type":"markdown","metadata":{"id":"w3bnXeuXM_am"},"source":["Creating custom graph dataset"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"k-Zv-fioPfd0"},"outputs":[],"source":["combined_phenotype='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","aug2_label = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/aug_labels.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","aug2_labels = pd.read_csv(aug2_label)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"4DazwG5AQoUn"},"outputs":[],"source":["def row_transform(arr, threshold):\n"," for i in range(len(arr)):\n"," arr[i] = arr[i] if arr[i]> threshold else abs(arr[i])+0.0001\n"," return arr\n","\n","def binarize(df, threshold):\n"," df = df.transform(lambda x: row_transform(x, threshold))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"eKnL6r1UxYBe"},"outputs":[],"source":["ub_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","\n","binary_features_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/UCLA Binary Local 0_2/'\n","weighted_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Weighted local feature files/'\n","\n","uba = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1 Binary 0_2'\n","uwa = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1'\n","\n","weighted_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features - UCLA Aug/'\n","binary_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug/'\n","\n","uba1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2 Binary 0_2/'\n","uwa1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2/'\n","\n","weighted_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features- UCLA Aug v2/'\n","binary_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug v2/'\n","\n","node2vec_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/node2vec/'"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0SHQCSrjwezy"},"outputs":[],"source":["graphs_dir = [uba1, uba, ub_02]\n","feat_dir = [(binary_features_02, \"binary_node_features_ucla_binary_\"), (weighted_features, \"weighted_node_features_\")]\n","aug_feat_dir = [(binary_features_aug, \"binary_node_features_\"), (weighted_features_aug, \"weighted_node_features_\")]\n","aug_feat_dir1 = [(binary_features_aug1, \"binary_node_features_\"), (weighted_features_aug1, \"weighted_node_features_\")]"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"80-tILrruzCv"},"outputs":[],"source":["graphs = list()\n","graph_labels = list()\n","\n","# Graph creation\n","for directory in graphs_dir:\n"," for file in os.listdir(directory):\n"," if '(' in file:\n"," continue\n"," if file.endswith('.csv'):\n"," if (directory == ub_02):\n"," subject = file[12:16]\n"," if int(subject) == 2155:\n"," continue\n"," elif (directory == uw):\n"," subject = file[14:18]\n"," elif (directory == uba):\n"," subject = file[12:16]\n"," if int(subject) < 3125:\n"," continue\n"," elif (directory == uba1):\n"," subject = file[12:16]\n"," else:\n"," print(\"INVALID DIRECTORY\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," subject = int(subject)\n"," print(subject)\n"," mask = labels_mappings['Subject'] == subject\n"," #only for aug v2\n"," if directory == uba1:\n"," if(labels_mappings[mask]['Label'].values[0]==0 or \n"," (labels_mappings[mask]['Label'].values[0]!=aug2_labels.query(\"Subject==@subject\")[\"assumed\"].values[0])):\n"," continue\n"," graph_labels.append(labels_mappings[mask]['Label'].values[0])\n","\n"," # APPENDING CORRESPONDING GRAPH\n"," df = pd.read_csv(directory+'/'+file, header=None)\n"," df = df.fillna(0)\n"," if directory == uba:\n"," for col in df:\n"," df[col] = df[col].astype(np.int64)\n"," G = nx.from_pandas_adjacency(df) \n","\n"," # Features\n"," if directory == uba: \n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir[1][0]+aug_feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n"," elif directory == uba1:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir1[1][0]+aug_feat_dir1[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True) \n"," else:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n","\n"," node_data = node_data.drop(['subgraph centrality'], axis=1, errors='ignore')\n","\n"," # Standardisation\n"," cols = list(node_data)\n"," scaler = StandardScaler().fit(node_data)\n"," node_data = scaler.transform(node_data)\n"," node_data = pd.DataFrame(node_data, columns = cols)\n"," \n"," g = StellarGraph.from_networkx(G,node_features=node_data)\n"," graphs.append(g)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"LUyZBt78mYP_"},"outputs":[],"source":["graph_labels = pd.DataFrame(graph_labels)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"jmGfxhMICpMq"},"outputs":[],"source":["graph_labels = pd.get_dummies(graph_labels, drop_first=True)"]},{"cell_type":"markdown","source":["## DGCNN 10 fold"],"metadata":{"id":"gaTt3ZDi0YlS"}},{"cell_type":"code","source":["generator = PaddedGraphGenerator(graphs=graphs)"],"metadata":{"id":"hKde6bl80pFi"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["acc = []\n","pre = []\n","re = []\n","spe = []\n","f = []\n","es = EarlyStopping(monitor=\"val_acc\", min_delta=0, patience=30, restore_best_weights=True)\n","epochs=100\n","for rs in range(1,11):\n"," k = 20 \n"," in_feat = 20\n"," layer_sizes = [in_feat, 32, 64, 128, 128, 64, 32, 16, 4, 2]\n"," dgcnn_model = DeepGraphCNN(\n"," layer_sizes=layer_sizes,\n"," activations=[\"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \n"," \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"softmax\"],\n"," k=k,\n"," bias=True,\n"," generator=generator,\n"," )\n"," x_inp, x_out = dgcnn_model.in_out_tensors()\n","\n"," x_out = Conv1D(filters=16, kernel_size=sum(layer_sizes), strides=sum(layer_sizes))(x_out)\n"," x_out = MaxPool1D(pool_size=2)(x_out)\n"," x_out = Conv1D(filters=32, kernel_size=4, strides=1)(x_out)\n"," x_out = Flatten()(x_out)\n"," x_out = Dense(units=128, activation=\"leaky_relu\")(x_out)\n"," x_out = Dropout(rate=0.5)(x_out)\n","\n"," predictions = Dense(units=1, activation=\"sigmoid\")(x_out)\n","\n"," model = Model(inputs=x_inp, outputs=predictions)\n"," model.compile(optimizer=Adam(learning_rate=0.0005), loss=binary_crossentropy, metrics=[\"acc\"],)\n","\n"," train_graphs, test_graphs = model_selection.train_test_split(graph_labels, train_size=0.8, test_size=0.2, stratify=graph_labels, random_state=rs)\n"," gen = PaddedGraphGenerator(graphs=graphs)\n","\n"," train_gen = gen.flow(\n"," list(train_graphs.index - 1),\n"," targets=train_graphs.values,\n"," batch_size=50,\n"," symmetric_normalization=True,\n"," )\n","\n"," test_gen = gen.flow(\n"," list(test_graphs.index - 1),\n"," targets=test_graphs.values,\n"," batch_size=1,\n"," symmetric_normalization=True,\n"," )\n","\n"," history = model.fit(train_gen, epochs=epochs, verbose=1, validation_data=test_gen, shuffle=True, callbacks=[es],)\n"," test_metrics = model.evaluate(test_gen)\n","\n"," pred = model.predict(test_gen)\n","\n"," y_pred = []\n"," y_true = []\n"," x = np.array(pred)\n"," for i in x:\n"," if i <0.5:\n"," y_pred.append(0)\n"," else:\n"," y_pred.append(1)\n","\n"," for t in test_gen.targets:\n"," y_true.append(t[0])\n","\n"," f1_score = metrics.f1_score(y_true, y_pred)\n"," precision = metrics.precision_score(y_true, y_pred)\n"," recall = metrics.recall_score(y_true, y_pred)\n"," accuracy = metrics.accuracy_score(y_true, y_pred)\n","\n"," if(accuracy >0.76):\n"," acc.append(accuracy)\n"," f.append(f1_score)\n"," pre.append(precision)\n"," re.append(recall)\n"," spe.append(specificity)\n","\n"," print('\\n\\n')\n","\n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(pre), np.std(pre)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(re), np.std(re)))\n","print('Average f1: %.3f +/- %.3f \\n\\n' %(np.mean(f), np.std(f)))\n","print('Average specificity: %.3f +/- %.3f \\n\\n' %(np.mean(spe), np.std(spe)))"],"metadata":{"id":"xhJTDhsViUw2"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["print(\"acc\")\n","print(np.mean(acc), \"±\", np.std(acc) )\n","\n","print(\"f1\")\n","print(np.mean(f), \"±\", np.std(f))\n","\n","print(\"rec\")\n","print(np.mean(pre), \"±\", np.std(pre) )\n","\n","print(\"prec\")\n","print(np.mean(re), \"±\" , np.std(re))\n","\n","print(\"spec\")\n","print(np.mean(spe), \"±\" , np.std(spe))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"VnaRAzaC3UnP","outputId":"baccafeb-9c64-45ed-f037-5107d1cd5b40"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["acc\n","0.79 ± 0.017320508075688742\n","f1\n","0.7673867125123706 ± 0.030863182475016307\n","rec\n","0.8597537878787879 ± 0.046276016898754074\n","prec\n","0.7000000000000001 ± 0.07211102550927981\n","spec\n","0.92 ± 0.0\n"]}]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/5. Graph Neural Network/DGCNN model.ipynb b/Code/5. Graph Neural Network/DGCNN model.ipynb new file mode 100644 index 0000000..d05a39f --- /dev/null +++ b/Code/5. Graph Neural Network/DGCNN model.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"ZO0efz7FKcNH","outputId":"3eee8019-bbcf-4baa-e727-2f974ff718de"},"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"34Sj6CEbxsHH","outputId":"499c3d43-97a7-4e45-94b5-3558b24901d8"},"outputs":[{"output_type":"stream","name":"stdout","text":["Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Collecting stellargraph\n"," Downloading stellargraph-1.2.1-py3-none-any.whl (435 kB)\n","\u001b[K |████████████████████████████████| 435 kB 9.1 MB/s \n","\u001b[?25hRequirement already satisfied: tensorflow>=2.1.0 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (2.9.2)\n","Requirement already satisfied: gensim>=3.4.0 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (3.6.0)\n","Requirement already satisfied: numpy>=1.14 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (1.21.6)\n","Requirement already satisfied: matplotlib>=2.2 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (3.2.2)\n","Requirement already satisfied: networkx>=2.2 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (2.6.3)\n","Requirement already satisfied: scikit-learn>=0.20 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (1.0.2)\n","Requirement already satisfied: scipy>=1.1.0 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (1.7.3)\n","Requirement already satisfied: pandas>=0.24 in /usr/local/lib/python3.7/dist-packages (from stellargraph) (1.3.5)\n","Requirement already satisfied: smart-open>=1.2.1 in /usr/local/lib/python3.7/dist-packages (from gensim>=3.4.0->stellargraph) 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pandas>=0.24->stellargraph) (2022.6)\n","Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.7/dist-packages (from scikit-learn>=0.20->stellargraph) (1.2.0)\n","Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.7/dist-packages (from scikit-learn>=0.20->stellargraph) (3.1.0)\n","Requirement already satisfied: tensorboard<2.10,>=2.9 in /usr/local/lib/python3.7/dist-packages (from tensorflow>=2.1.0->stellargraph) (2.9.1)\n","Requirement already satisfied: google-pasta>=0.1.1 in /usr/local/lib/python3.7/dist-packages (from tensorflow>=2.1.0->stellargraph) (0.2.0)\n","Requirement already satisfied: h5py>=2.9.0 in /usr/local/lib/python3.7/dist-packages (from tensorflow>=2.1.0->stellargraph) (3.1.0)\n","Requirement already satisfied: tensorflow-io-gcs-filesystem>=0.23.1 in /usr/local/lib/python3.7/dist-packages (from tensorflow>=2.1.0->stellargraph) (0.27.0)\n","Requirement already satisfied: absl-py>=1.0.0 in 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requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (3.2.2)\n","Installing collected packages: stellargraph\n","Successfully installed stellargraph-1.2.1\n","Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Requirement already satisfied: pyyaml in /usr/local/lib/python3.7/dist-packages (6.0)\n","Requirement already satisfied: h5py in /usr/local/lib/python3.7/dist-packages (3.1.0)\n","Requirement already satisfied: numpy>=1.14.5 in /usr/local/lib/python3.7/dist-packages (from h5py) (1.21.6)\n","Requirement already satisfied: cached-property in /usr/local/lib/python3.7/dist-packages (from h5py) (1.5.2)\n"]}],"source":["#installs\n","\n","!pip install stellargraph\n","!pip install pyyaml h5py"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OrtnMu3bNDm4"},"outputs":[],"source":["#imports \n","\n","from stellargraph import StellarGraph\n","import stellargraph as sg\n","from stellargraph.mapper import PaddedGraphGenerator\n","from stellargraph.layer import GCNSupervisedGraphClassification, DeepGraphCNN\n","import pandas as pd\n","import os\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","from sklearn.preprocessing import StandardScaler\n","from sklearn import model_selection\n","from IPython.display import display, HTML\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import math\n","from tensorflow.keras import Model\n","from tensorflow.keras.optimizers import Adam, SGD\n","from tensorflow.keras.layers import Dense, Conv1D, MaxPool1D, Dropout, Flatten\n","from tensorflow.keras.callbacks import EarlyStopping\n","from tensorflow.keras.layers import Dense\n","from tensorflow.keras.losses import binary_crossentropy\n","import tensorflow as tf\n","from tensorflow import keras\n","from sklearn.metrics import f1_score, precision_score, confusion_matrix, classification_report, confusion_matrix, ConfusionMatrixDisplay, roc_auc_score\n","import warnings\n","warnings.filterwarnings(\"ignore\")"]},{"cell_type":"markdown","metadata":{"id":"w3bnXeuXM_am"},"source":["Creating custom graph dataset"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"k-Zv-fioPfd0"},"outputs":[],"source":["combined_phenotype='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","aug2_label = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/aug_labels.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","aug2_labels = pd.read_csv(aug2_label)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"4DazwG5AQoUn"},"outputs":[],"source":["def row_transform(arr, threshold):\n"," for i in range(len(arr)):\n"," arr[i] = arr[i] if arr[i]> threshold else abs(arr[i])+0.0001\n"," return arr\n","\n","def binarize(df, threshold):\n"," df = df.transform(lambda x: row_transform(x, threshold))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"eKnL6r1UxYBe"},"outputs":[],"source":["ub_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","\n","binary_features_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/UCLA Binary Local 0_2/'\n","weighted_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Weighted local feature files/'\n","\n","uba = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1 Binary 0_2'\n","uwa = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1'\n","\n","weighted_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features - UCLA Aug/'\n","binary_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug/'\n","\n","uba1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2 Binary 0_2/'\n","uwa1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2/'\n","\n","weighted_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features- UCLA Aug v2/'\n","binary_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug v2/'\n","\n","node2vec_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/node2vec/'"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0SHQCSrjwezy"},"outputs":[],"source":["graphs_dir = [uba1, uba, ub_02]\n","feat_dir = [(binary_features_02, \"binary_node_features_ucla_binary_\"), (weighted_features, \"weighted_node_features_\")]\n","aug_feat_dir = [(binary_features_aug, \"binary_node_features_\"), (weighted_features_aug, \"weighted_node_features_\")]\n","aug_feat_dir1 = [(binary_features_aug1, \"binary_node_features_\"), (weighted_features_aug1, \"weighted_node_features_\")]"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"80-tILrruzCv","outputId":"c5d01082-4838-4e9b-94ef-003d6a1c2d96"},"outputs":[{"output_type":"stream","name":"stdout","text":["4018\n","4021\n","4023\n","4014\n","4016\n","4019\n","4024\n","4022\n","4025\n","4009\n","4017\n","4000\n","4001\n","4006\n","4015\n","4005\n","4002\n","4003\n","4013\n","4008\n","4010\n","4007\n","4020\n","4004\n","4011\n","4012\n","4041\n","4043\n","4061\n","4066\n","4034\n","4032\n","4051\n","4069\n","4067\n","4029\n","4035\n","4037\n","4028\n","4039\n","4062\n","4060\n","4038\n","4058\n","4047\n","4055\n","4072\n","4075\n","4050\n","4048\n","4074\n","4042\n","4068\n","4026\n","4073\n","4057\n","4054\n","4064\n","4052\n","4033\n","4030\n","4045\n","4071\n","4040\n","4056\n","4065\n","4063\n","4053\n","4031\n","4070\n","4036\n","4059\n","4027\n","4049\n","4044\n","4046\n","4098\n","4113\n","4103\n","4107\n","4077\n","4120\n","4100\n","4109\n","4080\n","4086\n","4091\n","4078\n","4079\n","4093\n","4112\n","4111\n","4090\n","4089\n","4104\n","4101\n","4108\n","4087\n","4083\n","4097\n","4123\n","4118\n","4117\n","4114\n","4124\n","4085\n","4099\n","4102\n","4116\n","4084\n","4119\n","4096\n","4088\n","4106\n","4105\n","4121\n","4094\n","4125\n","4092\n","4082\n","4110\n","4081\n","4115\n","4122\n","4095\n","4147\n","4076\n","4169\n","4129\n","4128\n","4144\n","4150\n","4141\n","4142\n","4154\n","4165\n","4143\n","4146\n","4151\n","4137\n","4161\n","4156\n","4157\n","4133\n","4135\n","4167\n","4136\n","4168\n","4164\n","4127\n","4170\n","4148\n","4171\n","4166\n","4153\n","4158\n","4159\n","4139\n","4162\n","4145\n","4163\n","4149\n","4140\n","4130\n","4134\n","4126\n","4131\n","4160\n","4155\n","4138\n","4152\n","4132\n","3125\n","3126\n","3129\n","3128\n","3130\n","3133\n","3131\n","3135\n","3132\n","3134\n","3136\n","3138\n","3137\n","3139\n","3140\n","3141\n","3142\n","3144\n","3143\n","3146\n","3145\n","3148\n","3149\n","3147\n","3151\n","3152\n","3154\n","3155\n","3153\n","3158\n","3156\n","3161\n","3159\n","3162\n","3157\n","3163\n","3164\n","3165\n","3168\n","3167\n","3170\n","3169\n","3171\n","3166\n","3160\n","3150\n","2019\n","2024\n","2022\n","2015\n","2017\n","2020\n","2025\n","2026\n","2023\n","2010\n","2018\n","2001\n","2002\n","2007\n","2016\n","2006\n","2014\n","2003\n","2004\n","2009\n","2008\n","2011\n","2005\n","2012\n","2021\n","2013\n","2042\n","2044\n","2067\n","2062\n","2035\n","2070\n","2033\n","2052\n","2030\n","2068\n","2029\n","2038\n","2036\n","2040\n","2063\n","2061\n","2059\n","2056\n","2039\n","2048\n","2073\n","2076\n","2051\n","2075\n","2043\n","2069\n","2049\n","2027\n","2074\n","2058\n","2055\n","2065\n","2034\n","2046\n","2053\n","2031\n","2072\n","2041\n","2057\n","2066\n","2064\n","2032\n","2054\n","2071\n","2037\n","2028\n","2060\n","2045\n","2047\n","2050\n","2099\n","2114\n","2108\n","2104\n","2101\n","2121\n","2078\n","2110\n","2081\n","2087\n","2092\n","2079\n","2113\n","2080\n","2094\n","2112\n","2091\n","2090\n","2105\n","2102\n","2088\n","2109\n","2124\n","2098\n","2084\n","2118\n","2119\n","2115\n","2125\n","2086\n","2100\n","2117\n","2103\n","2085\n","2097\n","2120\n","2107\n","2089\n","2106\n","2095\n","2126\n","2122\n","2093\n","2083\n","2111\n","2082\n","2123\n","2116\n","2096\n","2077\n","2148\n","2130\n","2171\n","2129\n","2151\n","2145\n","2142\n","2156\n","2143\n","2167\n","2144\n","2147\n","2152\n","2163\n","2138\n","2159\n","2158\n","2134\n","2169\n","2136\n","2137\n","2166\n","2128\n","2170\n","2149\n","2168\n","2160\n","2172\n","2154\n","2161\n","2140\n","2164\n","2165\n","2150\n","2146\n","2141\n","2131\n","2135\n","2127\n","2132\n","2157\n","2162\n","2139\n","2133\n","2153\n"]}],"source":["graphs = list()\n","graph_labels = list()\n","\n","# Graph creation\n","for directory in graphs_dir:\n"," for file in os.listdir(directory):\n"," if '(' in file:\n"," continue\n"," if file.endswith('.csv'):\n"," if (directory == ub_02):\n"," subject = file[12:16]\n"," if int(subject) == 2155:\n"," continue\n"," elif (directory == uw):\n"," subject = file[14:18]\n"," elif (directory == uba):\n"," subject = file[12:16]\n"," if int(subject) < 3125:\n"," continue\n"," elif (directory == uba1):\n"," subject = file[12:16]\n"," else:\n"," print(\"INVALID DIRECTORY\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," subject = int(subject)\n"," print(subject)\n"," mask = labels_mappings['Subject'] == subject\n"," #only for aug v2\n"," if directory == uba1:\n"," if(labels_mappings[mask]['Label'].values[0]==0 or \n"," (labels_mappings[mask]['Label'].values[0]!=aug2_labels.query(\"Subject==@subject\")[\"assumed\"].values[0])):\n"," continue\n"," graph_labels.append(labels_mappings[mask]['Label'].values[0])\n","\n"," # APPENDING CORRESPONDING GRAPH\n"," df = pd.read_csv(directory+'/'+file, header=None)\n"," df = df.fillna(0)\n"," if directory == uba:\n"," for col in df:\n"," df[col] = df[col].astype(np.int64)\n"," G = nx.from_pandas_adjacency(df) \n","\n"," # Features\n"," if directory == uba: \n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir[1][0]+aug_feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n"," elif directory == uba1:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir1[1][0]+aug_feat_dir1[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True) \n"," else:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n","\n"," node_data = node_data.drop(['subgraph centrality'], axis=1, errors='ignore')\n","\n"," # Standardisation\n"," cols = list(node_data)\n"," scaler = StandardScaler().fit(node_data)\n"," node_data = scaler.transform(node_data)\n"," node_data = pd.DataFrame(node_data, columns = cols)\n"," \n"," g = StellarGraph.from_networkx(G,node_features=node_data)\n"," graphs.append(g)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"LUyZBt78mYP_"},"outputs":[],"source":["graph_labels = pd.DataFrame(graph_labels)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Hap8HY-55Jqo","colab":{"base_uri":"https://localhost:8080/","height":143},"outputId":"926774b6-ea8d-4ac3-d13b-7c6d70d61d97"},"outputs":[{"output_type":"execute_result","data":{"text/plain":[" 0\n","0 \n","0 123\n","1 123"],"text/html":["\n","
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5s 692ms/step - loss: 0.6944 - acc: 0.4592 - val_loss: 0.6734 - val_acc: 0.6200\n","Epoch 2/100\n","4/4 [==============================] - 2s 407ms/step - loss: 0.6814 - acc: 0.5561 - val_loss: 0.6661 - val_acc: 0.7600\n","Epoch 3/100\n","4/4 [==============================] - 2s 408ms/step - loss: 0.6809 - acc: 0.6020 - val_loss: 0.6665 - val_acc: 0.6000\n","Epoch 4/100\n","4/4 [==============================] - 1s 391ms/step - loss: 0.6738 - acc: 0.6020 - val_loss: 0.6606 - val_acc: 0.5600\n","Epoch 5/100\n","4/4 [==============================] - 2s 410ms/step - loss: 0.6714 - acc: 0.5816 - val_loss: 0.6479 - val_acc: 0.7800\n","Epoch 6/100\n","4/4 [==============================] - 1s 392ms/step - loss: 0.6562 - acc: 0.6531 - val_loss: 0.6446 - val_acc: 0.7400\n","Epoch 7/100\n","4/4 [==============================] - 2s 421ms/step - loss: 0.6508 - acc: 0.6429 - val_loss: 0.6463 - val_acc: 0.6400\n","Epoch 8/100\n","4/4 [==============================] - 2s 403ms/step - loss: 0.6474 - acc: 0.6327 - val_loss: 0.6292 - val_acc: 0.7000\n","Epoch 9/100\n","4/4 [==============================] - 2s 510ms/step - loss: 0.6572 - acc: 0.5765 - val_loss: 0.6286 - val_acc: 0.7000\n","Epoch 10/100\n","4/4 [==============================] - 2s 432ms/step - loss: 0.6203 - acc: 0.6939 - val_loss: 0.6571 - val_acc: 0.5800\n","Epoch 11/100\n","4/4 [==============================] - 1s 348ms/step - loss: 0.6383 - acc: 0.6224 - val_loss: 0.6066 - val_acc: 0.7400\n","Epoch 12/100\n","4/4 [==============================] - 1s 395ms/step - loss: 0.6139 - acc: 0.6633 - val_loss: 0.5982 - val_acc: 0.7200\n","Epoch 13/100\n","4/4 [==============================] - 2s 530ms/step - loss: 0.6146 - acc: 0.6429 - val_loss: 0.5929 - val_acc: 0.7200\n","Epoch 14/100\n","4/4 [==============================] - 1s 363ms/step - loss: 0.6028 - acc: 0.6378 - val_loss: 0.5888 - val_acc: 0.7200\n","Epoch 15/100\n","4/4 [==============================] - 2s 557ms/step - loss: 0.6015 - acc: 0.6582 - val_loss: 0.6115 - val_acc: 0.6600\n","Epoch 16/100\n","4/4 [==============================] - 2s 637ms/step - loss: 0.6577 - acc: 0.5969 - val_loss: 0.5839 - val_acc: 0.7200\n","Epoch 17/100\n","4/4 [==============================] - 2s 407ms/step - loss: 0.5985 - acc: 0.6633 - val_loss: 0.5940 - val_acc: 0.7000\n","Epoch 18/100\n","4/4 [==============================] - 1s 375ms/step - loss: 0.5996 - acc: 0.6480 - val_loss: 0.6309 - val_acc: 0.6400\n","Epoch 19/100\n","4/4 [==============================] - 1s 358ms/step - loss: 0.5929 - acc: 0.6684 - val_loss: 0.5837 - val_acc: 0.7400\n","Epoch 20/100\n","4/4 [==============================] - 1s 358ms/step - loss: 0.5844 - acc: 0.6837 - val_loss: 0.5912 - val_acc: 0.7000\n","Epoch 21/100\n","4/4 [==============================] - 1s 381ms/step - loss: 0.5841 - acc: 0.6582 - val_loss: 0.5814 - val_acc: 0.7400\n","Epoch 22/100\n","4/4 [==============================] - 2s 410ms/step - loss: 0.5658 - acc: 0.6888 - val_loss: 0.5895 - val_acc: 0.6600\n","Epoch 23/100\n","4/4 [==============================] - 2s 494ms/step - loss: 0.5626 - acc: 0.6888 - val_loss: 0.5907 - val_acc: 0.6600\n","Epoch 24/100\n","4/4 [==============================] - 2s 429ms/step - loss: 0.5905 - acc: 0.6684 - val_loss: 0.5810 - val_acc: 0.7400\n","Epoch 25/100\n","4/4 [==============================] - 2s 419ms/step - loss: 0.5537 - acc: 0.7296 - val_loss: 0.6558 - val_acc: 0.6400\n","Epoch 26/100\n","4/4 [==============================] - 1s 372ms/step - loss: 0.5892 - acc: 0.6531 - val_loss: 0.5749 - val_acc: 0.7200\n","Epoch 27/100\n","4/4 [==============================] - 2s 522ms/step - loss: 0.5572 - acc: 0.6735 - val_loss: 0.6269 - val_acc: 0.6600\n","Epoch 28/100\n","4/4 [==============================] - 2s 429ms/step - loss: 0.5871 - acc: 0.6582 - val_loss: 0.5720 - val_acc: 0.7200\n","Epoch 29/100\n","4/4 [==============================] - 2s 669ms/step - loss: 0.5675 - acc: 0.6939 - val_loss: 0.6333 - val_acc: 0.6600\n","Epoch 30/100\n","4/4 [==============================] - 2s 574ms/step - loss: 0.5633 - acc: 0.6888 - val_loss: 0.5600 - val_acc: 0.7400\n","Epoch 31/100\n","4/4 [==============================] - 1s 355ms/step - loss: 0.5440 - acc: 0.7041 - val_loss: 0.6065 - val_acc: 0.6000\n","Epoch 32/100\n","4/4 [==============================] - 1s 362ms/step - loss: 0.5594 - acc: 0.7092 - val_loss: 0.5667 - val_acc: 0.7200\n","Epoch 33/100\n","4/4 [==============================] - 1s 399ms/step - loss: 0.5351 - acc: 0.7296 - val_loss: 0.6426 - val_acc: 0.6000\n","Epoch 34/100\n","4/4 [==============================] - 2s 519ms/step - loss: 0.5558 - acc: 0.7143 - val_loss: 0.5756 - val_acc: 0.7200\n","Epoch 35/100\n","4/4 [==============================] - 1s 359ms/step - loss: 0.5456 - acc: 0.7194 - val_loss: 0.6244 - val_acc: 0.6400\n","50/50 [==============================] - 0s 8ms/step - loss: 0.6479 - acc: 0.7800\n"]}],"source":["model = Model(inputs=x_inp, outputs=predictions)\n","model.compile(\n"," optimizer=Adam(learning_rate=0.0005), loss=binary_crossentropy, metrics=[\"acc\"],\n",")\n","\n","train_graphs, test_graphs = model_selection.train_test_split(graph_labels, train_size=0.80, test_size=0.20, stratify=graph_labels, random_state=3)\n","gen = PaddedGraphGenerator(graphs=graphs)\n","\n","train_gen = gen.flow(\n"," list(train_graphs.index - 1),\n"," targets=train_graphs.values,\n"," batch_size=50,\n"," symmetric_normalization=True,\n",")\n","\n","test_gen = gen.flow(\n"," list(test_graphs.index - 1),\n"," targets=test_graphs.values,\n"," batch_size=1,\n"," symmetric_normalization=True,\n",")\n","\n","history = model.fit(train_gen, epochs=epochs, verbose=1, validation_data=test_gen, shuffle=True, callbacks=[es],)\n","test_metrics = model.evaluate(test_gen)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"hgNzNEo3pOP9","outputId":"889d72cd-d0e4-444d-caa0-99ff6fe6d5db"},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","Test Set Metrics:\n","Validation Accuracy: 0.7799999713897705\n","Validation Loss: 0.5600392818450928\n"]}],"source":["print(\"\\nTest Set Metrics:\")\n","\n","print(\"Validation Accuracy: \", max(history.history['val_acc']))\n","print(\"Validation Loss: \", min(history.history['val_loss']))"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"EAjTlBZ8WOM3","outputId":"86461e1f-1785-4856-9f7b-dfff40267dc6"},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","Training Set Metrics:\n","Accuracy: 0.7295918464660645\n","Loss: 0.5350872874259949\n"]}],"source":["print(\"\\nTraining Set Metrics:\")\n","\n","print(\"Accuracy: \", max(history.history['acc']))\n","print(\"Loss: \", min(history.history['loss']))"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":295},"id":"p6mG-b0yPVvI","outputId":"2e89d376-3632-436b-e2cd-964240015c32"},"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}],"source":["plt.plot(history.history['acc'])\n","plt.plot(history.history['val_acc'])\n","plt.title('model accuracy')\n","plt.ylabel('accuracy')\n","plt.xlabel('epoch')\n","plt.legend(['train acc', 'val acc'], loc='upper left')\n","plt.show()"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FHHZOS3e0XN3","outputId":"835997c4-ef8f-44b7-8693-8afc28185a5e"},"outputs":[{"output_type":"stream","name":"stdout","text":["50/50 [==============================] - 1s 6ms/step\n"]}],"source":["pred = model.predict(test_gen)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"7a0R8L8G4j7P"},"outputs":[],"source":["y_pred = []\n","y_true = []\n","x = np.array(pred)\n","for i in x:\n"," if i <0.5:\n"," y_pred.append(0)\n"," else:\n"," y_pred.append(1)\n","\n","for t in test_gen.targets:\n"," y_true.append(t[0])"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"aIph_bQG5Xoo"},"outputs":[],"source":["from sklearn import metrics\n","\n","f1_score = metrics.f1_score(y_true, y_pred)\n","precision = metrics.precision_score(y_true, y_pred)\n","recall = metrics.recall_score(y_true, y_pred)\n","accuracy = metrics.accuracy_score(y_true, y_pred)\n","tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()\n","specificity = tn / (tn+fp)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"9jLoV_Out_Wi","outputId":"d45b7ed2-55ec-4ea5-a1aa-5b5a7b2e6d63"},"outputs":[{"output_type":"stream","name":"stdout","text":["Metrics:\n","Accuracy: 0.78\n","f1 score: 0.7555555555555556\n","precision: 0.85\n","recall: 0.68\n","specificity 0.88\n"]}],"source":["print(\"Metrics:\")\n","\n","print(\"Accuracy: \", accuracy)\n","print(\"f1 score: \", f1_score)\n","print(\"precision: \", precision)\n","print(\"recall: \", recall)\n","print(\"specificity \", specificity)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":297},"id":"x25DMyGRiCmJ","outputId":"7e4968d9-c4cc-47ed-c0fc-d0c27ecf2ee0"},"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{},"execution_count":136},{"output_type":"display_data","data":{"text/plain":["
"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}],"source":["disp = ConfusionMatrixDisplay(confusion_matrix=confusion_matrix(y_true, y_pred), display_labels=[0,1])\n","disp.plot()"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/5. Graph Neural Network/DGCNN with node2vec.ipynb b/Code/5. Graph Neural Network/DGCNN with node2vec.ipynb new file mode 100644 index 0000000..c7e5226 --- /dev/null +++ b/Code/5. Graph Neural Network/DGCNN with node2vec.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"id":"ZO0efz7FKcNH","colab":{"base_uri":"https://localhost:8080/"},"outputId":"cf5c1d7b-821d-4abb-e9bb-89717d1278a4"},"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"34Sj6CEbxsHH","outputId":"ce9f39fb-789e-4f5d-826c-280c08e31328"},"outputs":[{"output_type":"stream","name":"stdout","text":["Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Requirement already satisfied: stellargraph in /usr/local/lib/python3.8/dist-packages (1.2.1)\n","Requirement already satisfied: pandas>=0.24 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.3.5)\n","Requirement already satisfied: numpy>=1.14 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.21.6)\n","Requirement already satisfied: tensorflow>=2.1.0 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (2.9.2)\n","Requirement already satisfied: networkx>=2.2 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (2.8.8)\n","Requirement already satisfied: gensim>=3.4.0 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (3.6.0)\n","Requirement already satisfied: scipy>=1.1.0 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.7.3)\n","Requirement already satisfied: scikit-learn>=0.20 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (1.0.2)\n","Requirement already satisfied: matplotlib>=2.2 in /usr/local/lib/python3.8/dist-packages (from stellargraph) (3.2.2)\n","Requirement already satisfied: six>=1.5.0 in /usr/local/lib/python3.8/dist-packages (from gensim>=3.4.0->stellargraph) (1.15.0)\n","Requirement already satisfied: smart-open>=1.2.1 in 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(1.24.3)\n","Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.8/dist-packages (from requests<3,>=2.21.0->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (2022.9.24)\n","Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.8/dist-packages (from requests<3,>=2.21.0->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (3.0.4)\n","Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.8/dist-packages (from requests<3,>=2.21.0->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (2.10)\n","Requirement already satisfied: oauthlib>=3.0.0 in /usr/local/lib/python3.8/dist-packages (from requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.10,>=2.9->tensorflow>=2.1.0->stellargraph) (3.2.2)\n","Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Requirement already satisfied: pyyaml in /usr/local/lib/python3.8/dist-packages (6.0)\n","Requirement already satisfied: h5py in /usr/local/lib/python3.8/dist-packages (3.1.0)\n","Requirement already satisfied: numpy>=1.17.5 in /usr/local/lib/python3.8/dist-packages (from h5py) (1.21.6)\n","\u001b[K |████████████████████████████████| 135 kB 37.0 MB/s \n","\u001b[K |████████████████████████████████| 1.6 MB 47.1 MB/s \n","\u001b[?25h"]}],"source":["#installs\n","!pip install stellargraph\n","!pip install pyyaml h5py\n","!pip install -q -U keras-tuner"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OrtnMu3bNDm4"},"outputs":[],"source":["#imports \n","\n","from stellargraph import StellarGraph\n","import stellargraph as sg\n","from stellargraph.mapper import PaddedGraphGenerator\n","from stellargraph.layer import GCNSupervisedGraphClassification, DeepGraphCNN\n","import pandas as pd\n","import os\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","from sklearn.preprocessing import StandardScaler\n","from sklearn import model_selection\n","from IPython.display import display, HTML\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import math\n","from tensorflow.keras import Model\n","from tensorflow.keras.optimizers import Adam, SGD\n","from tensorflow.keras.layers import Dense, Conv1D, MaxPool1D, Dropout, Flatten\n","from tensorflow.keras.callbacks import EarlyStopping\n","from tensorflow.keras.layers import Dense\n","from tensorflow.keras.losses import binary_crossentropy\n","import tensorflow as tf\n","from tensorflow import keras\n","from sklearn.metrics import f1_score, precision_score, confusion_matrix, classification_report, confusion_matrix, ConfusionMatrixDisplay, roc_auc_score\n","import warnings\n","from sklearn import metrics\n","import keras_tuner as kt\n","warnings.filterwarnings(\"ignore\")"]},{"cell_type":"markdown","metadata":{"id":"w3bnXeuXM_am"},"source":["### Data Loading"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"k-Zv-fioPfd0"},"outputs":[],"source":["combined_phenotype='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","aug2_label = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/aug_labels.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","aug2_labels = pd.read_csv(aug2_label)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"4DazwG5AQoUn"},"outputs":[],"source":["def row_transform(arr, threshold):\n"," for i in range(len(arr)):\n"," arr[i] = arr[i] if arr[i]> threshold else abs(arr[i])+0.0001\n"," return arr\n","\n","def binarize(df, threshold):\n"," df = df.transform(lambda x: row_transform(x, threshold))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"eKnL6r1UxYBe"},"outputs":[],"source":["ub_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","\n","binary_features_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/UCLA Binary Local 0_2/'\n","weighted_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Weighted local feature files/'\n","\n","uba = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1 Binary 0_2'\n","uwa = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1'\n","\n","weighted_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features - UCLA Aug/'\n","binary_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug/'\n","\n","uba1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2 Binary 0_2/'\n","uwa1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2/'\n","\n","weighted_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features- UCLA Aug v2/'\n","binary_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug v2/'\n","\n","node2vec_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/node2vec/'"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0SHQCSrjwezy"},"outputs":[],"source":["graphs_dir = [uba1, uba, ub_02]\n","feat_dir = [(binary_features_02, \"binary_node_features_ucla_binary_\"), (weighted_features, \"weighted_node_features_\")]\n","aug_feat_dir = [(binary_features_aug, \"binary_node_features_\"), (weighted_features_aug, \"weighted_node_features_\")]\n","aug_feat_dir1 = [(binary_features_aug1, \"binary_node_features_\"), (weighted_features_aug1, \"weighted_node_features_\")]"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"80-tILrruzCv"},"outputs":[],"source":["graphs = list()\n","graph_labels = list()\n","\n","# Graph creation\n","for directory in graphs_dir:\n"," for file in os.listdir(directory):\n"," if '(' in file:\n"," continue\n"," if file.endswith('.csv'):\n"," if (directory == ub_02):\n"," subject = file[12:16]\n"," if int(subject) == 2155:\n"," continue\n"," elif (directory == uw):\n"," subject = file[14:18]\n"," elif (directory == uba):\n"," subject = file[12:16]\n"," if int(subject) < 3125:\n"," continue\n"," elif (directory == uba1):\n"," subject = file[12:16]\n"," else:\n"," print(\"INVALID DIRECTORY\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," subject = int(subject)\n"," print(subject)\n"," mask = labels_mappings['Subject'] == subject\n"," #only for aug v2\n"," if directory == uba1:\n"," if(labels_mappings[mask]['Label'].values[0]==0 or \n"," (labels_mappings[mask]['Label'].values[0]!=aug2_labels.query(\"Subject==@subject\")[\"assumed\"].values[0])):\n"," continue\n"," graph_labels.append(labels_mappings[mask]['Label'].values[0])\n","\n"," # APPENDING CORRESPONDING GRAPH\n"," df = pd.read_csv(directory+'/'+file, header=None)\n"," df = df.fillna(0)\n"," if directory == uba:\n"," for col in df:\n"," df[col] = df[col].astype(np.int64)\n"," G = nx.from_pandas_adjacency(df) \n","\n"," # Features\n"," if directory == uba: \n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir[1][0]+aug_feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n"," elif directory == uba1:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir1[1][0]+aug_feat_dir1[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True) \n"," else:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n","\n"," n2v_data = pd.read_csv(node2vec_features+ 'node2vec_features_ucla_binary_'+str(subject)+'.csv')\n"," n2v_data = n2v_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data,n2v_data, how = \"inner\", left_index=True, right_index=True)\n"," node_data = node_data.drop(['subgraph centrality'], axis=1, errors='ignore')\n","\n"," # Standardisation\n"," cols = list(node_data)\n"," scaler = StandardScaler().fit(node_data)\n"," node_data = scaler.transform(node_data)\n"," node_data = pd.DataFrame(node_data, columns = cols)\n"," \n"," g = StellarGraph.from_networkx(G,node_features=node_data)\n"," graphs.append(g)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"LUyZBt78mYP_"},"outputs":[],"source":["graph_labels = pd.DataFrame(graph_labels)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"jmGfxhMICpMq"},"outputs":[],"source":["graph_labels = pd.get_dummies(graph_labels, drop_first=True)"]},{"cell_type":"markdown","metadata":{"id":"-CufcfzeHY82"},"source":["## DGCNN Model with 10 fold cross validation"]},{"cell_type":"code","source":["generator = PaddedGraphGenerator(graphs=graphs)"],"metadata":{"id":"JT0TGVKIPUem"},"execution_count":null,"outputs":[]},{"cell_type":"code","execution_count":null,"metadata":{"id":"TPkT6Z3nv1Jv"},"outputs":[],"source":["epochs=100"]},{"cell_type":"code","source":["acc = []\n","spec = []\n","sens = []\n","prec = []\n","f1 = []"],"metadata":{"id":"N0QFwdVWL6CC"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for rs in list(range(1,10)):\n"," es = EarlyStopping(monitor=\"val_acc\", min_delta=0, patience=30, restore_best_weights=True, )\n","\n"," k = 20 \n"," in_feat = 27\n"," layer_sizes = [in_feat, 32, 64, 128, 128, 64, 32, 16, 4, 2]\n"," dgcnn_model = DeepGraphCNN(\n"," layer_sizes=layer_sizes,\n"," activations=[\"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"log_softmax\"],\n"," k=k,\n"," bias=True,\n"," generator=generator,\n"," )\n"," x_inp, x_out = dgcnn_model.in_out_tensors()\n","\n"," x_out = Conv1D(filters=16, kernel_size=sum(layer_sizes), strides=sum(layer_sizes))(x_out)\n"," x_out = MaxPool1D(pool_size=2)(x_out)\n"," x_out = Conv1D(filters=32, kernel_size=4, strides=1)(x_out)\n"," x_out = Flatten()(x_out)\n"," x_out = Dense(units=128, activation=\"leaky_relu\")(x_out)\n"," x_out = Dropout(rate=0.5)(x_out)\n","\n"," predictions = Dense(units=1, activation=\"sigmoid\")(x_out)\n","\n"," model = Model(inputs=x_inp, outputs=predictions)\n"," model.compile(optimizer=Adam(learning_rate=0.0005), loss=binary_crossentropy, metrics=[\"acc\"],)\n","\n"," train_graphs, test_graphs = model_selection.train_test_split(graph_labels, train_size=0.8, test_size=0.2, stratify=graph_labels, random_state=rs)\n"," gen = PaddedGraphGenerator(graphs=graphs)\n","\n"," train_gen = gen.flow(\n"," list(train_graphs.index - 1),\n"," targets=train_graphs.values,\n"," batch_size=50,\n"," symmetric_normalization=True,\n"," )\n","\n"," test_gen = gen.flow(\n"," list(test_graphs.index - 1),\n"," targets=test_graphs.values,\n"," batch_size=1,\n"," symmetric_normalization=True,\n"," )\n","\n"," history = model.fit(train_gen, epochs=epochs, verbose=1, validation_data=test_gen, shuffle=True, callbacks=[es],)\n"," test_metrics = model.evaluate(test_gen)\n"," pred = model.predict(test_gen)\n"," y_pred = []\n"," y_true = []\n"," x = np.array(pred)\n"," for i in x:\n"," if i <0.5:\n"," y_pred.append(0)\n"," else:\n"," y_pred.append(1)\n","\n"," for t in test_gen.targets:\n"," y_true.append(t[0])\n","\n"," accuracy = metrics.accuracy_score(y_true, y_pred)\n"," f1_score = metrics.f1_score(y_true, y_pred)\n"," precision = metrics.precision_score(y_true, y_pred)\n"," recall = metrics.recall_score(y_true, y_pred)\n"," tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()\n"," specificity = tn / (tn+fp)\n","\n"," acc.append(accuracy)\n"," spec.append(specificity)\n"," sens.append(recall)\n"," prec.append(precision)\n"," f1.append(f1_score)"],"metadata":{"id":"Q4oGKqxaBx7Z","executionInfo":{"status":"ok","timestamp":1678599227603,"user_tz":-330,"elapsed":3,"user":{"displayName":"GS_03 PW22","userId":"10516928092940211216"}}},"execution_count":1,"outputs":[]},{"cell_type":"code","source":["print(\"accuracy\")\n","print(np.mean(acc), \" +- \", np.std(acc))\n","print()\n","\n","print(\"specificity\")\n","print(np.mean(spec), \" +- \", np.std(spec))\n","print()\n","\n","print(\"sensitivity:\")\n","print(np.mean(sens), \" +- \", np.std(sens))\n","print()\n","\n","print(\"precision\")\n","print(np.mean(prec), \" +- \", np.std(prec))\n","print()\n","\n","print(\"f1\")\n","print(np.mean(f1), \" +- \", np.std(f1))\n","print()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"DJDPOT7OIEp0","outputId":"85be68d8-1de6-4e08-d3b8-5c2a0f9d44bf"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["accuracy\n","0.8049999999999999 +- 0.021794494717703346\n","\n","specificity\n","0.745 +- 0.05634713834792323\n","\n","sensitivity:\n","0.865 +- 0.03427827300200523\n","\n","precision\n","0.7746346911029892 +- 0.0350793599648721\n","\n","f1\n","0.8161985673306428 +- 0.017452551539528235\n","\n"]}]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/5. Graph Neural Network/GCN model 10 fold CV.ipynb b/Code/5. Graph Neural Network/GCN model 10 fold CV.ipynb new file mode 100644 index 0000000..54aa2ef --- /dev/null +++ b/Code/5. Graph Neural Network/GCN model 10 fold CV.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"id":"ZO0efz7FKcNH"},"outputs":[],"source":["from google.colab import drive\n","drive.mount('/content/drive')"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"34Sj6CEbxsHH"},"outputs":[],"source":["#installs\n","!pip install stellargraph\n","!pip install pyyaml h5py"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OrtnMu3bNDm4"},"outputs":[],"source":["#imports \n","\n","from stellargraph import StellarGraph\n","import stellargraph as sg\n","from stellargraph.mapper import PaddedGraphGenerator\n","from stellargraph.layer import GCNSupervisedGraphClassification, DeepGraphCNN\n","import pandas as pd\n","import os\n","import numpy as np\n","import networkx as nx\n","import matplotlib.pyplot as plt\n","from sklearn.preprocessing import StandardScaler\n","from sklearn import model_selection\n","from IPython.display import display, HTML\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import math\n","from tensorflow.keras import Model\n","from tensorflow.keras.optimizers import Adam, SGD\n","from tensorflow.keras.layers import Dense, Conv1D, MaxPool1D, Dropout, Flatten\n","from tensorflow.keras.callbacks import EarlyStopping\n","from tensorflow.keras.layers import Dense\n","from tensorflow.keras.losses import binary_crossentropy\n","import tensorflow as tf\n","from tensorflow import keras\n","from sklearn.metrics import f1_score, precision_score, confusion_matrix, classification_report, confusion_matrix, ConfusionMatrixDisplay, roc_auc_score\n","import warnings\n","warnings.filterwarnings(\"ignore\")"]},{"cell_type":"markdown","metadata":{"id":"w3bnXeuXM_am"},"source":["### Loading Data"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"s51S4IlaPnle"},"outputs":[],"source":["combined_phenotype='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","aug2_label = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/aug_labels.csv'\n","labels_mappings= pd.read_csv(combined_phenotype)\n","aug2_labels = pd.read_csv(aug2_label)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"4DazwG5AQoUn"},"outputs":[],"source":["def row_transform(arr, threshold):\n"," for i in range(len(arr)):\n"," arr[i] = arr[i] if arr[i]> threshold else abs(arr[i])+0.0001\n"," return arr\n","\n","def binarize(df, threshold):\n"," df = df.transform(lambda x: row_transform(x, threshold))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"eKnL6r1UxYBe"},"outputs":[],"source":["ub_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","\n","binary_features_02 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/UCLA Binary Local 0_2/'\n","weighted_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Weighted local feature files/'\n","\n","uba = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1 Binary 0_2'\n","uwa = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1'\n","\n","weighted_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features - UCLA Aug/'\n","binary_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug/'\n","\n","uba1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2 Binary 0_2/'\n","uwa1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2/'\n","\n","weighted_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features- UCLA Aug v2/'\n","binary_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug v2/'\n","\n","node2vec_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/node2vec/'"]},{"cell_type":"code","source":["graphs_dir = [uba1, uba, ub_02]\n","feat_dir = [(binary_features_02, \"binary_node_features_ucla_binary_\"), (weighted_features, \"weighted_node_features_\")]\n","aug_feat_dir = [(binary_features_aug, \"binary_node_features_\"), (weighted_features_aug, \"weighted_node_features_\")]\n","aug_feat_dir1 = [(binary_features_aug1, \"binary_node_features_\"), (weighted_features_aug1, \"weighted_node_features_\")]"],"metadata":{"id":"aT7b-jlwqJ4W"},"execution_count":null,"outputs":[]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ikl0M337zW3q"},"outputs":[],"source":["in_feat=0"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"80-tILrruzCv"},"outputs":[],"source":["graphs = list()\n","graph_labels = list()\n","\n","# Graph creation\n","for directory in graphs_dir:\n"," for file in os.listdir(directory):\n"," if '(' in file:\n"," continue\n"," if file.endswith('.csv'):\n"," if (directory == ub_02):\n"," subject = file[12:16]\n"," if int(subject) == 2155:\n"," continue\n"," elif (directory == uw):\n"," subject = file[14:18]\n"," elif (directory == uba):\n"," subject = file[12:16]\n"," if int(subject) < 3125:\n"," continue\n"," elif (directory == uba1):\n"," subject = file[12:16]\n"," else:\n"," print(\"INVALID DIRECTORY\")\n"," exit(0)\n","\n"," # APPENDING LABEL\n"," subject = int(subject)\n"," print(subject)\n"," mask = labels_mappings['Subject'] == subject\n"," #only for aug v2\n"," if directory == uba1:\n"," if(labels_mappings[mask]['Label'].values[0]==0 or \n"," (labels_mappings[mask]['Label'].values[0]!=aug2_labels.query(\"Subject==@subject\")[\"assumed\"].values[0])):\n"," continue\n"," graph_labels.append(labels_mappings[mask]['Label'].values[0])\n","\n"," # APPENDING CORRESPONDING GRAPH\n"," df = pd.read_csv(directory+'/'+file, header=None)\n"," df = df.fillna(0)\n"," if directory == uba:\n"," for col in df:\n"," df[col] = df[col].astype(np.int64)\n"," G = nx.from_pandas_adjacency(df) \n","\n"," # Features\n"," if directory == uba: \n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir[0][0]+aug_feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir[1][0]+aug_feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n"," elif directory == uba1:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else: \n"," node_data_1 = pd.read_csv(aug_feat_dir1[0][0]+aug_feat_dir1[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir1[1][0]+aug_feat_dir1[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True) \n"," else:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n","\n"," node_data = node_data.drop(['subgraph centrality'], axis=1, errors='ignore')\n","\n"," # Standardisation\n"," cols = list(node_data)\n"," scaler = StandardScaler().fit(node_data)\n"," node_data = scaler.transform(node_data)\n"," node_data = pd.DataFrame(node_data, columns = cols)\n"," \n"," g = StellarGraph.from_networkx(G,node_features=node_data)\n"," graphs.append(g)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"LUyZBt78mYP_"},"outputs":[],"source":["graph_labels = pd.DataFrame(graph_labels)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"jmGfxhMICpMq"},"outputs":[],"source":["graph_labels = pd.get_dummies(graph_labels, drop_first=True)"]},{"cell_type":"markdown","metadata":{"id":"-CufcfzeHY82"},"source":["### GCN Model"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"05KvxfZfC0s1"},"outputs":[],"source":["generator = PaddedGraphGenerator(graphs=graphs)"]},{"cell_type":"code","source":["from sklearn import metrics\n","acc = []\n","pre = []\n","re = []\n","spe = []\n","f = []\n","es = EarlyStopping(monitor=\"val_acc\", min_delta=0, patience=30, restore_best_weights=True)\n","epochs=100\n","for rs in list(range(1,11)):\n"," print(rs)\n"," gc_model = GCNSupervisedGraphClassification(\n"," layer_sizes=[in_feat, 32, 64, 128, 64, 32, 16, 4, 2],\n"," activations=[\"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"leaky_relu\", \"log_softmax\"],\n"," generator=generator,\n"," pool_all_layers = True,\n"," pooling = None,\n"," dropout=0.5,\n"," )\n"," x_inp, x_out = gc_model.in_out_tensors()\n","\n"," predictions = Dense(units=16, activation=\"relu\")(x_out)\n"," #predictions = Dense(units=16, activation=\"relu\")(predictions)\n"," predictions = Dense(units=1, activation=\"sigmoid\")(predictions)\n","\n"," model = Model(inputs=x_inp, outputs=predictions)\n"," model.compile(\n"," optimizer=Adam(learning_rate=0.0005), loss=binary_crossentropy, metrics=[\"acc\"],\n"," )\n","\n"," train_graphs, test_graphs = model_selection.train_test_split(graph_labels, train_size=0.8, test_size=0.2, stratify=graph_labels, random_state=rs)\n"," gen = PaddedGraphGenerator(graphs=graphs)\n","\n"," train_gen = gen.flow(\n"," list(train_graphs.index - 1),\n"," targets=train_graphs.values,\n"," batch_size=50,\n"," symmetric_normalization=True,\n"," )\n","\n"," test_gen = gen.flow(\n"," list(test_graphs.index - 1),\n"," targets=test_graphs.values,\n"," batch_size=1,\n"," symmetric_normalization=True,\n"," )\n","\n"," history = model.fit(train_gen, epochs=epochs, verbose=1, validation_data=test_gen, shuffle=True, callbacks=[es],)\n"," test_metrics = model.evaluate(test_gen)\n","\n"," print(\"\\nTest Set Metrics:\")\n"," print(\"Validation Accuracy: \", max(history.history['val_acc']))\n"," print(\"Validation Loss: \", min(history.history['val_loss']))\n","\n"," print(\"\\nTraining Set Metrics:\")\n"," print(\"Accuracy: \", max(history.history['acc']))\n"," print(\"Loss: \", min(history.history['loss']))\n","\n"," pred = model.predict(test_gen)\n","\n"," y_pred = []\n"," y_true = []\n"," x = np.array(pred)\n"," for i in x:\n"," if i <0.5:\n"," y_pred.append(0)\n"," else:\n"," y_pred.append(1)\n","\n"," for t in test_gen.targets:\n"," y_true.append(t[0])\n","\n"," print(confusion_matrix(y_true, y_pred))\n","\n","\n"," f1_score = metrics.f1_score(y_true, y_pred)\n"," precision = metrics.precision_score(y_true, y_pred)\n"," recall = metrics.recall_score(y_true, y_pred)\n"," accuracy = metrics.accuracy_score(y_true, y_pred)\n","\n"," print(\"Metrics:\")\n"," print(\"Accuracy: \", accuracy)\n"," print(\"f1 score: \", f1_score)\n"," print(\"precision: \", precision)\n"," print(\"recall: \", recall)\n"," tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()\n"," specificity = tn / (tn+fp)\n"," print(\"Specificity\", specificity)\n","\n"," acc.append(accuracy)\n"," f.append(f1_score)\n"," pre.append(precision)\n"," re.append(recall)\n"," spe.append(specificity)\n","\n"," print('\\n\\n')\n","\n","print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(pre), np.std(pre)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(re), np.std(re)))\n","print('Average f1: %.3f +/- %.3f \\n\\n' %(np.mean(f), np.std(f)))\n","print('Average specificity: %.3f +/- %.3f \\n\\n' %(np.mean(spe), np.std(spe)))"],"metadata":{"id":"bajZBv5rDQDB"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["print('Average accccuracy: %.3f +/- %.3f' %(np.mean(acc), np.std(acc)))\n","print('Average precision: %.3f +/- %.3f' %(np.mean(pre), np.std(pre)))\n","print('Average recall: %.3f +/- %.3f' %(np.mean(re), np.std(re)))\n","print('Average f1: %.3f +/- %.3f \\n\\n' %(np.mean(f), np.std(f)))\n","print('Average specificity: %.3f +/- %.3f \\n\\n' %(np.mean(spe), np.std(spe)))"],"metadata":{"id":"OTCmkjKJxeI9"},"execution_count":null,"outputs":[]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/6. Biomarker Detection/RLF feature selection.ipynb b/Code/6. Biomarker Detection/RLF feature selection.ipynb new file mode 100644 index 0000000..a416cd1 --- /dev/null +++ b/Code/6. Biomarker Detection/RLF feature selection.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# IMPORT"],"metadata":{"id":"zYu8Z-ZZR9c5"}},{"cell_type":"code","source":["!pip install shap"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"_R1hOUD974fE","outputId":"2112d4a2-ed4e-404c-cb1e-bd1f87743f3b"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n","Requirement already satisfied: shap in /usr/local/lib/python3.8/dist-packages (0.41.0)\n","Requirement already satisfied: pandas in /usr/local/lib/python3.8/dist-packages (from shap) (1.3.5)\n","Requirement already satisfied: scikit-learn in /usr/local/lib/python3.8/dist-packages (from shap) (1.0.2)\n","Requirement already satisfied: numba in /usr/local/lib/python3.8/dist-packages (from shap) (0.56.4)\n","Requirement already satisfied: cloudpickle in /usr/local/lib/python3.8/dist-packages (from shap) (1.5.0)\n","Requirement already satisfied: slicer==0.0.7 in /usr/local/lib/python3.8/dist-packages (from shap) (0.0.7)\n","Requirement already satisfied: tqdm>4.25.0 in /usr/local/lib/python3.8/dist-packages (from shap) (4.64.1)\n","Requirement already satisfied: scipy in /usr/local/lib/python3.8/dist-packages (from shap) (1.7.3)\n","Requirement already satisfied: numpy in /usr/local/lib/python3.8/dist-packages (from shap) (1.21.6)\n","Requirement already satisfied: packaging>20.9 in /usr/local/lib/python3.8/dist-packages (from shap) (21.3)\n","Requirement already satisfied: pyparsing!=3.0.5,>=2.0.2 in /usr/local/lib/python3.8/dist-packages (from packaging>20.9->shap) (3.0.9)\n","Requirement already satisfied: importlib-metadata in /usr/local/lib/python3.8/dist-packages (from numba->shap) (5.1.0)\n","Requirement already satisfied: llvmlite<0.40,>=0.39.0dev0 in /usr/local/lib/python3.8/dist-packages (from numba->shap) (0.39.1)\n","Requirement already satisfied: setuptools in /usr/local/lib/python3.8/dist-packages (from numba->shap) (57.4.0)\n","Requirement already satisfied: zipp>=0.5 in /usr/local/lib/python3.8/dist-packages (from importlib-metadata->numba->shap) (3.11.0)\n","Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.8/dist-packages (from pandas->shap) (2022.6)\n","Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.8/dist-packages (from pandas->shap) (2.8.2)\n","Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.7.3->pandas->shap) (1.15.0)\n","Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.8/dist-packages (from scikit-learn->shap) (1.2.0)\n","Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.8/dist-packages (from scikit-learn->shap) (3.1.0)\n"]}]},{"cell_type":"code","execution_count":null,"metadata":{"id":"69SRlXYeGKo7"},"outputs":[],"source":["import os\n","import pandas as pd \n","import numpy as np\n","from sklearn import preprocessing,svm\n","from sklearn.metrics import confusion_matrix,classification_report,accuracy_score, mean_absolute_error, mean_squared_error,f1_score\n","from sklearn.neighbors import KNeighborsRegressor\n","from sklearn.preprocessing import StandardScaler, Normalizer\n","from itertools import product, combinations\n","from sklearn.tree import DecisionTreeClassifier\n","from sklearn.naive_bayes import GaussianNB\n","from sklearn.ensemble import AdaBoostClassifier\n","from sklearn.linear_model import LogisticRegression\n","from sklearn.neighbors import KNeighborsClassifier\n","from sklearn.svm import SVC, LinearSVC\n","from sklearn.ensemble import VotingClassifier,RandomForestClassifier,GradientBoostingClassifier\n","from sklearn.model_selection import GridSearchCV, cross_val_score, StratifiedKFold, train_test_split\n","from sklearn.feature_selection import mutual_info_classif,SelectFromModel\n","from sklearn.decomposition import PCA\n","import itertools\n","import matplotlib.pyplot as plt\n","from sklearn.pipeline import Pipeline\n","import cvxopt\n","import matplotlib.mlab as mlab\n","import seaborn\n","import pickle\n","import pandas as pd\n","import numpy as np\n","import os\n","import matplotlib.pyplot as plt\n","from sklearn.feature_selection import mutual_info_classif,SelectFromModel\n","from sklearn.svm import LinearSVC\n","from itertools import combinations\n","from sklearn.decomposition import PCA\n","import time\n","import shap\n","\n","%matplotlib inline"]},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive', force_remount = False)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"sOI8I6fOQ8nG","outputId":"38e257e3-63c6-4b38-a661-60357fee8a99"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"]}]},{"cell_type":"markdown","source":["# DATA CREATION"],"metadata":{"id":"kQ6EuK3WSBfu"}},{"cell_type":"code","source":["# Labels\n","combined_phenotype= '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","\n","labels_mappings= pd.read_csv(combined_phenotype)\n","labels_mappings"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":424},"id":"U-MOCXi4b0Uq","outputId":"4d0d0aca-3dbf-47e8-f20c-e5cbf13d3bb6"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" Subject Label\n","0 40013 0\n","1 40014 0\n","2 40017 0\n","3 40018 0\n","4 40019 0\n",".. ... ...\n","759 4167 0\n","760 4168 0\n","761 4169 1\n","762 4170 1\n","763 4171 1\n","\n","[764 rows x 2 columns]"],"text/html":["\n","
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.........
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if(int(sub)<2000):\n"," continue\n"," r = df.index[df.Subject == sub]\n"," mask = labels_mappings['Subject'] == sub\n"," df.at[r, 'Schizophrenic'] = labels_mappings[mask]['Label'].values[0]"],"metadata":{"id":"WiL5Cx45bYHE"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["#take care of subject 3127\n","r = df.index[df.Subject == 3127]\n","df=df.drop(r)"],"metadata":{"id":"QCy1wSAByld4"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# MODEL"],"metadata":{"id":"9UWMk7_OR7I_"}},{"cell_type":"code","source":["df_original= df[(df['Subject'] < 3000)]"],"metadata":{"id":"ik5I22Yb3Br4"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df_original.fillna(0, inplace=True)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"LalrdYhi6MDv","outputId":"77b1a100-3913-4708-acf8-fd463d8a0c1b"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stderr","text":["\n","A value is trying to be set on a copy of a slice from a DataFrame\n","\n","See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n"]}]},{"cell_type":"code","source":["df_original.to_csv('merged features.csv')"],"metadata":{"id":"vPTsyxKnfAph"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["X = df_original.drop(['Schizophrenic'], axis=1)\n","X = X.drop(['Subject'], axis=1)\n","y = df_original['Schizophrenic']"],"metadata":{"id":"Kka2iGjL1tn3"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Feature Selection"],"metadata":{"id":"8CMwNwIt6sq-"}},{"cell_type":"code","source":["importances = mutual_info_classif(X,y)\n","feat_importances = pd.Series(importances, df.columns[0:len(df.columns)-2])"],"metadata":{"id":"0YhQ6Jfc2mpY"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["feat_importances.sort_values(ascending=False, inplace=True) "],"metadata":{"id":"VAhCeuq-3ke5"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["feat_importances = feat_importances.to_frame()\n","feat_importances['name'] = feat_importances.index\n","feat = feat_importances.head(50)"],"metadata":{"id":"r9Bf0ujh202f"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["feat.reset_index(drop=True, inplace=True)\n","feat"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"id":"uB6v8a-c0W1U","outputId":"a9ec3a33-57c8-44a6-f997-97a721ec1cb8"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" 0 name\n","0 0.192734 142_avg neighbour degree\n","1 0.161039 117_load centrality\n","2 0.160579 112_local clustering\n","3 0.159658 152_betweenness centrality\n","4 0.159655 85_load centrality\n","5 0.158532 73_square clustering\n","6 0.156196 122_number of cliques\n","7 0.154679 70_degree\n","8 0.151850 70_degree centrality\n","9 0.149884 116_harmonic centrality\n","10 0.147656 117_betweenness centrality\n","11 0.147299 4_betweenness centrality\n","12 0.147121 98_avg neighbour degree\n","13 0.146528 4_load centrality\n","14 0.146192 159_current flow betweenness centrality\n","15 0.145864 71_constraint\n","16 0.142928 24_betweenness centrality\n","17 0.142557 134_local clustering\n","18 0.142309 116_local reaching centrality\n","19 0.140472 27_number of cliques\n","20 0.139788 145_closeness centrality\n","21 0.139707 38_load centrality\n","22 0.137201 72_harmonic centrality\n","23 0.137016 129_second order clustering\n","24 0.136679 40_local reaching centrality\n","25 0.135739 131_second order clustering\n","26 0.135112 112_information centrality\n","27 0.134260 72_local reaching centrality\n","28 0.133751 152_load centrality\n","29 0.133307 156_current flow betweenness centrality\n","30 0.132711 33_avg neighbour degree\n","31 0.132209 80_closeness centrality\n","32 0.131608 121_number of cliques\n","33 0.131547 72_information centrality\n","34 0.130861 140_current flow betweenness centrality\n","35 0.130840 131_pagerank centrality\n","36 0.130364 4_current flow betweenness centrality\n","37 0.129774 129_eigenvector centrality\n","38 0.129728 85_betweenness centrality\n","39 0.127852 92_load centrality\n","40 0.127110 147_number of cliques\n","41 0.126709 66_number of cliques\n","42 0.126589 145_harmonic centrality\n","43 0.125919 144_pagerank centrality\n","44 0.125479 133_information centrality\n","45 0.125366 40_harmonic centrality\n","46 0.125098 9_betweenness centrality\n","47 0.124383 60_degree centrality\n","48 0.124158 140_eccentricity\n","49 0.124052 30_degree"],"text/html":["\n","
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0name
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30.159658152_betweenness centrality
40.15965585_load centrality
50.15853273_square clustering
60.156196122_number of cliques
70.15467970_degree
80.15185070_degree centrality
90.149884116_harmonic centrality
100.147656117_betweenness centrality
110.1472994_betweenness centrality
120.14712198_avg neighbour degree
130.1465284_load centrality
140.146192159_current flow betweenness centrality
150.14586471_constraint
160.14292824_betweenness centrality
170.142557134_local clustering
180.142309116_local reaching centrality
190.14047227_number of cliques
200.139788145_closeness centrality
210.13970738_load centrality
220.13720172_harmonic centrality
230.137016129_second order clustering
240.13667940_local reaching centrality
250.135739131_second order clustering
260.135112112_information centrality
270.13426072_local reaching centrality
280.133751152_load centrality
290.133307156_current flow betweenness centrality
300.13271133_avg neighbour degree
310.13220980_closeness centrality
320.131608121_number of cliques
330.13154772_information centrality
340.130861140_current flow betweenness centrality
350.130840131_pagerank centrality
360.1303644_current flow betweenness centrality
370.129774129_eigenvector centrality
380.12972885_betweenness centrality
390.12785292_load centrality
400.127110147_number of cliques
410.12670966_number of cliques
420.126589145_harmonic centrality
430.125919144_pagerank centrality
440.125479133_information centrality
450.12536640_harmonic centrality
460.1250989_betweenness centrality
470.12438360_degree centrality
480.124158140_eccentricity
490.12405230_degree
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\n"," "]},"metadata":{},"execution_count":109}]},{"cell_type":"code","source":["biomarkers_dict = {str(key):0.0 for key in list(range(164))}"],"metadata":{"id":"KTUZz0u62i1A"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for ind, row in feat.iterrows():\n"," roi = row['name'][0:3]\n"," if roi[-2]=='_':\n"," roi = roi[0:1]\n"," if roi[-1]=='_':\n"," roi = roi[0:2]\n"," biomarkers_dict[roi]= biomarkers_dict[roi]+ row[0]"],"metadata":{"id":"YV5SrLbK1STU"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["biomarkers_max = sorted(biomarkers_dict.items(), key=lambda y: y[1], reverse=True)[:10]"],"metadata":{"id":"8G0T9eye4-kV"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["biomarkers_max"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Gn2DIRkJGKk-","outputId":"ebf126da-7d62-4552-a110-50a352af4d00"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[('4', 0.42419045658287424),\n"," ('72', 0.4030090549376779),\n"," ('117', 0.30869550002416357),\n"," ('70', 0.30652885240809113),\n"," ('112', 0.2956906831739914),\n"," ('152', 0.2934084818614171),\n"," ('116', 0.2921933897272986),\n"," ('85', 0.289382321283999),\n"," ('129', 0.26679037775859005),\n"," ('131', 0.26657903351546497)]"]},"metadata":{},"execution_count":118}]},{"cell_type":"code","source":["biomarkers = [i[0] for i in biomarkers_max]"],"metadata":{"id":"NAjb1kuoF77O"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["biomarkers"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"GprIoNwfGC0r","outputId":"76d9c9d3-d26a-419d-a031-f413be28de2e"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["['4', '72', '117', '70', '112', '152', '116', '85', '129', '131']"]},"metadata":{},"execution_count":123}]},{"cell_type":"markdown","source":["Given ROIs above are potential biomarkers\n"],"metadata":{"id":"wjVYR-faHHjC"}}]} \ No newline at end of file diff --git a/Code/6. Biomarker Detection/SpeCo.ipynb b/Code/6. Biomarker Detection/SpeCo.ipynb new file mode 100644 index 0000000..fda2cb5 --- /dev/null +++ b/Code/6. Biomarker Detection/SpeCo.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","metadata":{"id":"lfcTzZ1R1Fsu"},"source":["# IMPORTS"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"cTkcnh6DzouG"},"outputs":[],"source":["import pandas as pd\n","import networkx as nx \n","import matplotlib.pyplot as plt\n","from networkx.algorithms.community.centrality import girvan_newman\n","from sklearn import preprocessing\n","import os\n","import random\n","import numpy as np\n","from sklearn.cluster import KMeans\n","import matplotlib.patches as mpatches\n"]},{"cell_type":"markdown","metadata":{"id":"KTANL1bT1SZA"},"source":["# DATA LOADING"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"p0EosiGa1Rws","outputId":"e87368a1-510c-4b46-e4f3-e5f830545b33"},"outputs":[{"name":"stdout","output_type":"stream","text":["Mounted at /content/drive\n"]}],"source":["from google.colab import drive\n","drive.mount('/content/drive', force_remount=False)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"1QuioiIQ2Brz"},"outputs":[],"source":["ub = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Binary 0_2'\n","uw = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Weighted v2'\n","\n","binary_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/UCLA Binary Local 0_2/'\n","weighted_features = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Weighted local feature files/'\n","\n","uwa = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1'\n","uba = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v1 Binary 0_2'\n","\n","weighted_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features - UCLA Aug/'\n","binary_features_aug = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug/'\n","\n","uba1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2 Binary 0_2/'\n","uwa1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Preprocessed Data/UCLA Augmented v2/'\n","\n","weighted_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Weighted features- UCLA Aug v2/'\n","binary_features_aug1 = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Generated Features/Local Binary features - UCLA Aug v2/'"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":419},"id":"2jW18L9b2Hce","outputId":"c81eec84-c406-48cb-a2f6-92daf666639b"},"outputs":[{"data":{"text/html":["\n","
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SubjectSubject TypeLabel
040013Control0
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240017Control0
340018Control0
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............
5873167Control1
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5913171Patient1
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\n"," "],"text/plain":[" Subject Subject Type Label\n","0 40013 Control 0\n","1 40014 Control 0\n","2 40017 Control 0\n","3 40018 Control 0\n","4 40019 Control 0\n",".. ... ... ...\n","587 3167 Control 1\n","588 3168 Control 1\n","589 3169 Patient 1\n","590 3170 Patient 1\n","591 3171 Patient 1\n","\n","[592 rows x 3 columns]"]},"execution_count":4,"metadata":{},"output_type":"execute_result"}],"source":["# Labels\n","combined_phenotype='/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/phenotypic_data.csv'\n","\n","labels_mappings= pd.read_csv(combined_phenotype)\n","labels_mappings"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0EWzbCGp2J5Z"},"outputs":[],"source":["graphs_dir = [ub, uba]\n","feat_dir = [(weighted_features, \"weighted_node_features_\"), (binary_features, \"binary_node_features_\")]\n","aug_feat_dir = [(weighted_features_aug, \"weighted_node_features_\"), (binary_features_aug, \"binary_node_features_\")]"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"NTlc9ifa2Ovq"},"outputs":[],"source":["class SyntheticDataset():\n"," def __init__(self, gclasses, dim_nfeats):\n"," self.gclasses = gclasses\n"," self.dim_nfeats = dim_nfeats\n"," self.process()\n"," \n"," def process(self):\n"," self.graphs = []\n"," self.labels = []\n"," \n"," # Graph creation\n"," for ind in range(len(graphs_dir)):\n"," directory = graphs_dir[ind]\n"," for file in os.listdir(directory):\n"," if '(' in file:\n"," continue \n"," if file.endswith('.csv'):\n"," if (directory == cb):\n"," subject = file[13:18]\n"," elif (directory == cw):\n"," subject = file[15:20]\n"," elif (directory == ub):\n"," subject = file[12:16]\n"," elif (directory == uw):\n"," subject = file[14:18]\n"," elif (directory == uwa):\n"," subject = file[14:18]\n"," elif (directory == uba):\n"," subject = file[12:16]\n"," if int(subject) < 3122:\n"," continue\n"," else:\n"," print(\"INVALID DIRECTORY\")\n"," exit(0)\n"," \n","\n"," # APPENDING LABEL\n"," mask = labels_mappings['Subject'] == int(subject)\n"," self.labels.append(labels_mappings[mask]['Label'].values[0])\n","\n"," # APPENDING CORRESPONDING GRAPH\n"," df = pd.read_csv(directory+'/'+file, header=None)\n"," df = df.fillna(0)\n"," G = nx.from_pandas_adjacency(df) \n","\n"," # Features\n"," if directory == uwa or directory == uba:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(aug_feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(aug_feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(aug_feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n"," else:\n"," if len(feat_dir) == 1:\n"," node_data = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data = node_data.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," else:\n"," node_data_1 = pd.read_csv(feat_dir[0][0]+feat_dir[0][1]+str(subject)+'.csv')\n"," node_data_2 = pd.read_csv(feat_dir[1][0]+feat_dir[1][1]+str(subject)+'.csv')\n"," node_data_1 = node_data_1.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data_2 = node_data_2.drop(['Unnamed: 0'], axis=1, errors='ignore')\n"," node_data = pd.merge(node_data_1, node_data_2, how = \"inner\", left_index=True, right_index=True)\n","\n"," node_data = node_data.drop(['subgraph centrality'], axis=1, errors='ignore')\n","\n"," # Standardisation\n"," cols = list(node_data)\n"," scaler = preprocessing.StandardScaler().fit(node_data)\n"," node_data = scaler.transform(node_data)\n"," node_data = pd.DataFrame(node_data, columns = cols)\n","\n","\n"," dict_list = dict()\n"," for index, rows in node_data.iterrows():\n"," dict_list[index] = list(rows)\n","\n"," count=0\n"," for col in node_data:\n"," nx.set_node_attributes(G, dict_list[count], 'attrs')\n"," count+=1\n"," \n"," self.graphs.append(G)\n"," \n"," def __getitem__(self, i):\n"," return self.graphs[i], self.labels[i]\n"," \n"," def __len__(self):\n"," return len(self.graphs)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"metJZoC63lyx"},"outputs":[],"source":["dataset = SyntheticDataset(2, 25)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":419},"id":"lpgVDa3JoUVL","outputId":"7cc5202e-193e-49f2-8ab1-44bf5b28f178"},"outputs":[{"data":{"text/html":["\n","
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ROIRegion
00DefaultMode.MPFC (1,55,-3)
11DefaultMode.LP (L) (-39,-77,33)
22DefaultMode.LP (R) (47,-67,29)
33DefaultMode.PCC (1,-61,38)
44SensoriMotor.Lateral (L) (-55,-12,29)
.........
159159Ver6 (Vermis 6)
160160Ver7 (Vermis 7)
161161Ver8 (Vermis 8)
162162Ver9 (Vermis 9)
163163Ver10 (Vermis 10)
\n","

164 rows × 2 columns

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\n","
\n"," "],"text/plain":[" ROI Region\n","0 0 DefaultMode.MPFC (1,55,-3)\n","1 1 DefaultMode.LP (L) (-39,-77,33)\n","2 2 DefaultMode.LP (R) (47,-67,29)\n","3 3 DefaultMode.PCC (1,-61,38)\n","4 4 SensoriMotor.Lateral (L) (-55,-12,29)\n",".. ... ...\n","159 159 Ver6 (Vermis 6)\n","160 160 Ver7 (Vermis 7)\n","161 161 Ver8 (Vermis 8)\n","162 162 Ver9 (Vermis 9)\n","163 163 Ver10 (Vermis 10)\n","\n","[164 rows x 2 columns]"]},"execution_count":11,"metadata":{},"output_type":"execute_result"}],"source":["aal_path = '/content/drive/MyDrive/SUPPLEMENTARY CODE/Data/Metadata/CONN ROIS - Mappings.csv'\n","aal = pd.read_csv(aal_path)\n","aal"]},{"cell_type":"markdown","metadata":{"id":"3aEF85IrLiOh"},"source":["# SpeCo SPECTRAL CLUSTERING with CO-OCCURENCE MATRIX"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"EqY2VcT8jRPr"},"outputs":[],"source":["# Class to perform spectral clustering for k clusters, given k\n","\n","class SpectralClustering:\n"," \n"," def __init__(self, G):\n"," # Initialize the graph, nodes and the normalized Laplacian\n","\n"," self.graph = G\n"," self.normalized_laplacian = nx.linalg.normalized_laplacian_matrix(G).toarray()\n"," self.nodes = G.nodes()\n","\n"," def compute_eigenspace(self):\n"," # Compute the eigenvalues and the eigenvectors using Numpy and sort them in ascending order \n","\n"," eigenvalues, eigenvectors = np.linalg.eig(self.normalized_laplacian)\n","\n"," sort_index = np.argsort(eigenvalues) # Returns the list of indices that would sort the array\n"," sorted_eigenvectors = eigenvectors[:, sort_index]\n","\n"," return sorted_eigenvectors\n","\n"," def fit(self, k):\n"," \"\"\"\n"," Step 1: Extract the k eigen vectors and stack them vertically to form a matrix (i.e each vector is a column)\n"," Step 2: Every row of this matrix represents the features of the respective nodes of the graph\n"," Step 3: Perform K-Means clustering on this dataset to identify k clusters\n","\n"," \"\"\"\n"," eigenvectors = self.compute_eigenspace()\n"," k_eigenvectors = np.array(eigenvectors)[:,:k]\n"," dataset = pd.DataFrame(k_eigenvectors, index=self.nodes)\n","\n"," # print(dataset)\n","\n"," k_means_clusters = KMeans(n_clusters = k, random_state=42)\n"," self.clusters = k_means_clusters.fit(k_eigenvectors)\n"," \n"," def predict_labels(self):\n"," # Returns the labels \n"," return self.clusters.labels_\n","\n"," def assign_labels(self, labels):\n"," # Helper to assign the labels as node attributes\n"," for i,node in enumerate(self.graph.nodes()):\n"," self.graph.nodes[node]['label'] = labels[i]\n","\n"," def plot_graph(self, n_clusters, title='Graph after Spectral Clustering'):\n"," # Plots the graph \n","\n"," labels = self.clusters.labels_\n"," self.assign_labels(labels)\n","\n"," colour_list = ['lightgreen','red','yellow', 'magenta','lightblue','grey']\n"," sampled_colours = dict(zip(set(labels),random.sample(colour_list, n_clusters)))\n","\n"," legend_handles = []\n"," for label, color in sampled_colours.items():\n"," colour_handle = mpatches.Patch(color=color, label=label)\n"," legend_handles.append(colour_handle)\n","\n"," colours = [sampled_colours[i] for i in labels]\n","\n"," pos_fr = nx.fruchterman_reingold_layout(self.graph)\n"," plt.figure(figsize=(16,14))\n"," plt.title(title)\n"," plt.legend(handles=legend_handles)\n"," nx.draw(self.graph, pos=pos_fr, node_size=700, node_color=colours, with_labels=True)\n"," plt.show()"]},{"cell_type":"markdown","metadata":{"id":"nnJV4ly2RSqB"},"source":["### PRELIMINARY"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"2Sp3_AhRMHPQ"},"outputs":[],"source":["# Performing Spectral Clustering on the graph\n","k = 4\n","\n","G = dataset[0][0]\n","SpecClust = SpectralClustering(G)\n","SpecClust.fit(k)\n","clustering_labels = SpecClust.predict_labels()\n","# print(labels)\n","\n","for i,node in enumerate(G.nodes()):\n"," G.nodes[node]['label'] = clustering_labels[i]\n","\n","colour_map = ['']*len(clustering_labels)\n","for i, label in enumerate(clustering_labels):\n"," if label == 0:\n"," colour_map[i] = 'lightgreen'\n"," else:\n"," colour_map[i] = \"red\"\n","\n","# nx.draw(CG, with_labels=True, node_color=colour_map)\n","SpecClust.plot_graph(k, title=\"Graph after Spectral Clustering\")"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"EZSGye_oMMnk"},"outputs":[],"source":["# Performing Spectral Clustering on the graph\n","k = 2\n","schiz_comm = dict()\n","control_comm = dict()\n","\n","for i in range(164):\n"," schiz_comm[i] = {0:0, 1:0}\n"," control_comm[i] = {0:0, 1:0}\n","\n","for i in dataset:\n"," G = i[0]\n"," sch = i[1]\n"," SpecClust = SpectralClustering(G)\n"," SpecClust.fit(k)\n"," clustering_labels = SpecClust.predict_labels()\n","\n"," if sch:\n"," for i in range(len(clustering_labels)):\n"," schiz_comm[i][clustering_labels[i]] += 1\n"," else:\n"," for i in range(len(clustering_labels)):\n"," control_comm[i][clustering_labels[i]] += 1"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"zPk8sEyqRp4O"},"outputs":[],"source":["schiz_comm"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"tFCaOWrHVQzi"},"outputs":[],"source":["control_comm"]},{"cell_type":"markdown","metadata":{"id":"WovjIxidRjWq"},"source":["### MAIN"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"_PSwAM3Hdta-"},"outputs":[],"source":["sc_results = dict()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"sopVS_kDlp_B"},"outputs":[],"source":["confidence = 0.95"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Qez6tel9ZW7D"},"outputs":[],"source":["k = 2"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"KmMEZTlUWhVS"},"outputs":[],"source":["cooccurance_schiz = np.zeros((164,164))\n","cooccurance_control = np.zeros((164,164))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"xuSJx1ZEYAsy"},"outputs":[],"source":["# Performing Spectral Clustering on the graph\n","\n","for i in dataset:\n"," G = i[0]\n"," sch = i[1]\n"," SpecClust = SpectralClustering(G)\n"," SpecClust.fit(k)\n"," clustering_labels = SpecClust.predict_labels()\n","\n"," if sch:\n"," for x in range(len(clustering_labels)):\n"," for y in range(x+1, len(clustering_labels)):\n"," if clustering_labels[x] == clustering_labels[y]:\n"," cooccurance_schiz[x][y] += 1\n"," cooccurance_schiz[y][x] += 1\n"," else:\n"," for x in range(len(clustering_labels)):\n"," for y in range(x+1, len(clustering_labels)):\n"," if clustering_labels[x] == clustering_labels[y]:\n"," cooccurance_control[x][y] += 1\n"," cooccurance_control[y][x] += 1"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"TbJ-i4h4ZILa"},"outputs":[],"source":["cooccurance_schiz"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"msuApcm3ZKkA"},"outputs":[],"source":["cooccurance_control"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"yZ9Kf_taaCcY"},"outputs":[],"source":["cooccurance_schiz_bool = np.zeros((164,164))\n","cooccurance_control_bool = np.zeros((164,164))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"xqMuIEBrZUKM"},"outputs":[],"source":["for x in range(164):\n"," for y in range(x+1, 164):\n"," if cooccurance_schiz[x][y] > dataset.labels.count(1)*confidence:\n"," cooccurance_schiz_bool[x][y] += 1\n"," cooccurance_schiz_bool[y][x] += 1"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"_HaaFtfHbk6A"},"outputs":[],"source":["for x in range(164):\n"," for y in range(x+1, 164):\n"," if cooccurance_control[x][y] > dataset.labels.count(0)*confidence:\n"," cooccurance_control_bool[x][y] += 1\n"," cooccurance_control_bool[y][x] += 1"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"tSsqStPjavxm"},"outputs":[],"source":["pd.DataFrame(cooccurance_schiz_bool)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"UR7gFQdZbPXk"},"outputs":[],"source":["pd.DataFrame(cooccurance_control_bool)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"OdesSrKIb0ap"},"outputs":[],"source":["count = 0\n","for x in range(164):\n"," for y in range(x+1, 164):\n"," if cooccurance_schiz_bool[x][y] != cooccurance_control_bool[x][y]:\n"," count += 1\n"," print(x, aal[aal['ROI'] == x]['Region'].item(), y, aal[aal['ROI'] == y]['Region'].item(), sep='\\t\\t')\n","print(count)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"SO1_Syt0dpD5"},"outputs":[],"source":["sc_results[k] = count"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Vt8L2bv5d1ce"},"outputs":[],"source":["sc_results"]},{"cell_type":"markdown","metadata":{"id":"X6FQYYu0KWkG"},"source":["**ANALYSIS** \n"," \n"," \n","k = 3 \n","90% CI \n","\n","4\t5:\tSensoriMotor.Lateral (L) (-55,-12,29),\tSensoriMotor.Lateral (R) (56,-10,29) \n","*Motor: Lack of motor skill is a symptom of schiz* \n"," \n","7\t97:\tVisual.Medial (2,-79,12), LG r (Lingual Gyrus Right) \n","*LG: Visuals, especially reading letters. Also logical orders and visual memories.* \n"," \n","20 67:\tDorsalAttention.IPS (L) (-39,-43,52), SPL l (Superior Parietal Lobule Left) \n","*SPL: attention and visuospatial perception, including the representation and manipulation of objects, DA IPS: voluntary orienting of visuospatial attention, selection of stimuli based on current internal goals or expectations and pre-existing information about presented stimuli.* \n"," \n","25\t72:\tFrontoParietal.PPC (R) (52,-52,45),\tAG r (Angular Gyrus Right) \n","31 139:\tCerebellar.Posterior (0,-79,-32), Cereb1 r (Cerebelum Crus1 Right) \n","105\t106: OFusG r (Occipital Fusiform Gyrus Right),\tOFusG l (Occipital Fusiform Gyrus Left) \n","117\t118: PT r (Planum Temporale Right), PT l (Planum Temporale Left) \n"," \n"," \n"," \n","k = 2 \n","95% CI \n"," \n","31\t\tCerebellar.Posterior (0,-79,-32)\t\t140\t\tCereb2 l (Cerebelum Crus2 Left) \n","34\t\tIC r (Insular Cortex Right)\t\t35\t\tIC l (Insular Cortex Left) \n","44\t\tPreCG r (Precentral Gyrus Right)\t\t45\t\tPreCG l (Precentral Gyrus Left) \n","109\t\tCO r (Central Opercular Cortex Right)\t\t110\t\tCO l (Central Opercular Cortex Left) \n","109\t\tCO r (Central Opercular Cortex Right)\t\t118\t\tPT l (Planum Temporale Left) \n","110\t\tCO l (Central Opercular Cortex Left)\t\t117\t\tPT r (Planum Temporale Right) \n","112\t\tPO l (Parietal Operculum Cortex Left)\t\t118\t\tPT l (Planum Temporale Left) \n","113\t\tPP r (Planum Polare Right)\t\t114\t\tPP l (Planum Polare Left) \n","117\t\tPT r (Planum Temporale Right)\t\t118\t\tPT l (Planum Temporale Left) \n"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file diff --git a/Code/README.md.docx b/Code/README.md.docx new file mode 100644 index 0000000000000000000000000000000000000000..e73070cd29307aaa3f1aad7a8a05bb35724b2721 GIT binary patch literal 8702 zcmaJ`WmsIxvc=tl6Wlcf4Q_!za3357hr!)FI6(#p5G=U6WN=S#3GNcy0>R}$?tS;< z{ua+?W9yk^E7xAxZDSUC_MZAu#GVZfI6Y68JX<^hqN{o8t^;yji}{| z-u11Y=dxe2zFWX=gS!X9;B-0rgV|JmT%A>qkQ6`8mk^w7N~<}^)?t4T$(NNg{Gtj8uSdcZ9}S$XupfeZNLZe;9p_9aEfd1O zgM~^<7#Onfkp_9A$*}q63?+SS{;g{}Q%{|Mz`OpuBj{SzkSZbhp}Z^Lti)~`hBEW) zk@X;M1DfUfR;h{gB$OFKfP?kjvYyWKFb6IpfBNpMl<`i*k=AFDA!O_Y&bk2zM|l^A z?_8y#5sA!=Ho;PJ<7qS0J?lqo+fg3+yU{7&HReFgCX`UoVX?~ioIPkq3^5pi!K$by~XLTG;QmzjE55QJi2Uep&pwEUqUEfbuT7y4cZ2I=eW+i2ptq ziIe^a>qn_QbD?u`RCxBnbXKlSN__y`VV;NaGm3)uWNS3;$9re#pl;DE64uMuLe+N` zpV;fBN=AYlsLXbv5YEFGfeOged=j)UDe3HY_6z>`3(T2bpgDLva+>qbAABKb`OEu; z?di*!&~9g^HqB-=`IqljKIvNL2Q(uFkg&5sT?)aKAIHTXQ7E#ba~7FLpQ4Ae7ovx~ z$~{+o03|I&4YWebQp z;`$A#g3rDi4fIU-&ZKm_n5XaqQ{1LG)nOUnX15e^gM1x)zHTtl^WF%Dwfav<%t?Gq z46FIr=dqio0sjP!&Ls}<4%A-7w zU^8z$q@~*RLGYR<*tkM7!s(mx59YaL8Do)7O{)vcryPo@>B@zNfr8pa_@^BD&t5mP zvvpQ80)k9`B@y`dy`GDN6(P+G7l;moeQs!<-rac)FfPb$=(9Oh)ke-U!s|)6XgRs; zaVxPa%c-NFA2R{HR0PnV_35T^7?U3<*685#VbURnNST1BpX;!`I83b-UDw0i=*>$t zFa5EU@38Mq%hkxIZ6sbLI=<4yoLGf$U3?JrseWa%KyBP^ZGfi9h!ufTBSA)|TTWJC zyYg5^CPI?3$%6c2VDIH2?fZUf)~IE^UK+J+=;)GM7gBk}yb$0wu_-?rV43=bo^fB} zCY<~$)UtCabQN3VCVRG0;loHFhqx%h75p*g-rD2&n!VRSTta4PQPfIDLYPYjqppQU z)Lks;#1s9kXH+7{7EW{Uaw%KcOJ9{4g{j~YD~d2TaN#Qay%CjEkx;IZ`^no&voW3Y zVS0YYeTS)IgPG8!gP4v3ulH}3 zueO{VcfSqkNPEiC(3nkfUneJxNlY3G=Q~Ybo?g4Z)>>^X~i99 zB_F$Q>BmH$y+s_L;tfn4M^!@l5%2K&=SEaG7MLuei6{{8`nJ=U5;3G8#juXYW`LOJ z1DaE`^r#G-12#~R{fils>xar&G%tpmFG8;q8jA*CPjj%86JK+|Q}H88nff;ke(S8a z^5p23Oggdw62*HjM(~DzM+NM3A;}P1^aPKgcu45JOBYaAr+W|Sp7V(|7gMtZI z?5rkh;|$1nRWDrj(X^@RX8YfT(8%M+6l5H$`2#d-{P6`F?)YrgdT8Mf@~D(?O-PVm zKxI2Zk4pux+XdWuWyvx`%x3a3ZNKW($oysJ|<=3n=;4SLDkCW zRuDZmg}#p|LT9)IGkp!c&3ObpL_zhoSK>t0qzeST733&3vEzo`G1@0?fC<8AOLcd& z_7^SI2{#(RT~N^~mE@&WkDYb8@Xi9nSz|Kj7||^FmW$8*RUE~u z*2(kfxHxp*H?K)3R9F%=KkV1XYOTgM)7J)TI~@#*b^q)M0&su0UWN2J>AwHcdN--s z7J<`?D-N~`&5s{i2=X0Aq>**SaB`-{VmXX$J(lFx&=Bg8>5`+oBRiPa zXwI~(p5cBz;Q6o-Nwut&Z>-MDS!bheL{fOJUwE!1MjDkW{xK;LwLd6zFLMqfSa1f_ z!+tKd4-$1yA0;G}!m#U#<;Og-FN6u+j$16Ucu1J^`SZdTkMU-RBi+g#L9^i~(|Z z2KO~*PXTgR`|sBXg6s6h466NdfjiyB9a%2*I{Nq=g5o6qrkMQhd(Vh(pFIFB zezd?~j$9b1bd)ly$}y_O%^(-UpNRll@nR&6UWtXrg-1yomcZmyt=mnE+ef?saU#V) zWjqBYZXWgsIf1g-XhK#^E+eL)498lPaY2h+ucKpW+nAKsc6-;#kfzEt9keWzd4i1{ ziG|d$GU~T4^_}7LS|Ak zwID@M!zDt&Lv8KhkuR1hr(v{tXu)gib?`nuvAsBVJwhNz#2t>YN(lHdstgHwUJR7x z=n<^_+{P~`5mWV=_O*WwS#gmV!F`9nSY|XO&!A|T@-(GK8Fti+1k{1 zpQv>q)GTPZ!6KUcA*htB140@pa@gz02bsY1Vgy++Szww9Cz@qyPpy`obTNzYp|fsj z5k)<+p?ea^1}^{U=uiEJ`L(pR(2Mjp{eGvJx9#_K+7j6~B{kmULdFp@;=J_4!yp%? 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