NCP_plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "\n",
    "\n",
    "import pdb\n",
    "\n",
    "from NCP_plots import build_nbd_hypergraph, sample_cuts_from_all_nodes\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Karate Club"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.karate_club_graph()\n",
    "n = len(G.nodes())\n",
    "hgraph = build_nbd_hypergraph(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_min_envelope(phi_by_k_dict, name):\n",
    "    k_list = list(phi_by_k_dict.keys())\n",
    "    min_pts = [min(phi_by_k_dict[k]) for k in k_list]\n",
    "    max_k_to_plot = int(len(k_list)/2)+1\n",
    "    plt.plot(k_list[:max_k_to_plot], min_pts[:max_k_to_plot],'-o', color='red')\n",
    "\n",
    "    ax = plt.gca()\n",
    "    ax.set_xlabel('k')\n",
    "    ax.set_ylabel('Conductance')\n",
    "    ax.set_yscale('log')\n",
    "    ax.set_xscale('log')\n",
    "\n",
    "    # Add-ons specific to different graphs\n",
    "    if name=='karate_club':\n",
    "        plt.axvline(x = 5, color='blue', ls='--', label = 'k=5')\n",
    "        plt.axvline(x = 17, color='green',ls='--', label = 'k=17')\n",
    "        ax.set_ylim(bottom=0.1, top=1)\n",
    "        plt.title('Karate club')\n",
    "        filename = 'karate_club_hypergraph_NCP.pdf'\n",
    "    elif name=='dolphins':\n",
    "        plt.axvline(x = 21, color='blue', ls='--', label = 'k=21')\n",
    "        ax.set_ylim(bottom=0.01,top=1)\n",
    "        ax.set_xlim(right=100)\n",
    "        plt.title('Dolphins')\n",
    "        filename = 'dolphins_hypergraph_NCP.pdf'\n",
    "\n",
    "    ax.set_aspect('equal')\n",
    "    plt.legend()\n",
    "    plt.savefig('./NCP_figures/'+filename, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
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      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.092    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.303    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
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      "     1.169    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.964    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.888    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.844    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
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      "     0.847    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
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      "     0.758    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.814    100      0.000000       0.000000\n",
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      "     0.775    100      0.000000       0.000000\n",
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      "     0.768    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.873    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.929    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
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      "     0.741    100      0.000000       0.000000\n",
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      "     0.743    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.965    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.808    100      0.000000       0.000000\n",
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      "     0.779    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.736    100      0.000000       0.000000\n",
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      "     0.745    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.845    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.830    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.975    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     1.033    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.825    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.820    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.805    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.914    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.851    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
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      "     0.819    100      0.000000       0.000000\n",
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      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.848    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.962    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.799    100      0.000000       0.000000\n",
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      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 5.588. Average rank = 5.588\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     0.818    100      0.000000       0.000000\n",
      "iterate = 99\n"
     ]
    }
   ],
   "source": [
    "phi_by_k, best_cut_by_k = sample_cuts_from_all_nodes(hgraph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_min_envelope(phi_by_k, name='karate_club')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "    # W, sparse_h, rank = compute_hypergraph_matrices(n, m, hypergraph, weights=None)\n",
    "    # hypergraph_cut_objective = lambda vec: eval_hypergraph_cut_fn(\n",
    "    #     hypergraph_objective, vec, s_vector, sparse_h, rank, W, D\n",
    "    # )\n",
    "    # hypergraph_diff_results = dict(\n",
    "    #     {\n",
    "    #         \"x\": x,\n",
    "    #         \"y\": y,\n",
    "    #         \"fx\": fx,\n",
    "    #         \"objective\": hypergraph_cut_objective,\n",
    "    #         \"type\": \"hypergraph\",\n",
    "    #     }\n",
    "    # )\n",
    "\n",
    "    # # now run the vanilla graph diffusion\n",
    "    # # STEP SIZE 1/2\n",
    "    # # compute degree from weighted matrix? or use combinatorial degree (as we do with hypergraphs)?\n",
    "    # graph_D = np.squeeze(np.asarray(np.sum(knn_adj_matrix, axis=0)))\n",
    "    # x, y, fx = graph_diffusion(\n",
    "    #     x0,\n",
    "    #     graph_D,\n",
    "    #     knn_adj_matrix,\n",
    "    #     s=s_vector,\n",
    "    #     h=0.5,\n",
    "    #     T=num_iterations,\n",
    "    #     verbose=verbose,\n",
    "    # )\n",
    "\n",
    "    # graph_cut_objective = lambda vec: eval_graph_cut_fn(\n",
    "    #     graph_D, knn_adj_matrix, s_vector, vec\n",
    "    # )\n",
    "    # graph_diff_results = dict(\n",
    "    #     {\"x\": x, \"y\": y, \"fx\": fx, \"objective\": graph_cut_objective, \"type\": \"graph\"}\n",
    "    # )\n",
    "\n",
    "    # return hypergraph_diff_results, graph_diff_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dolphins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.621    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.568    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.552    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.343    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.237    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.265    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.554    100      0.000001       0.000004\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.349    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.338    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.324    100      0.000001       0.000005\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.335    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.664    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.406    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.545    100      0.000001       0.000007\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.306    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.312    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.371    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.284    100      0.000001       0.000007\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.640    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.785    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.351    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.317    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.336    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.382    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.473    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.315    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.310    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.343    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.313    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.306    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.289    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.299    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.427    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.330    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.331    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.431    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.318    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.288    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.289    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.302    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.294    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.300    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.381    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.292    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.305    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.295    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.423    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.302    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.298    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.301    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.408    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.328    100      0.000000       0.000002\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.433    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.320    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.322    100      0.000000       0.000003\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.307    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.310    100      0.000000       0.000001\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.294    100      0.000001       0.000006\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.333    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.476    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.330    100      0.000000       0.000000\n",
      "iterate = 99\n",
      "Warning: lamda <= 0. This will ignore the provided labels.\n",
      "Average degree = 6.129. Average rank = 6.129\n",
      "  Time (s) # Iter    ||dx||_D^2        F(x(t))\n",
      "     1.350    100      0.000000       0.000000\n",
      "iterate = 99\n"
     ]
    }
   ],
   "source": [
    "G = nx.convert_node_labels_to_integers(nx.read_gml('./data/dolphins.gml'))\n",
    "n = len(G.nodes())\n",
    "hgraph = build_nbd_hypergraph(G)\n",
    "phi_by_k, best_cut_by_k = sample_cuts_from_all_nodes(hgraph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u4XiReOJM7m1sDP1TjY19/yzJpKiJqRV42MzOMbNzgH8HViYXltSdYsMIBg2CwYO77hs2LBxb6hyAnTvVGd7PRUpM7v5VYClwcK58xd3/NcnApM4Ue+rKt78NK1Z03ZffsV14zr77hv3t7YmNc/rYx0KRZGkSr9SOCROKDylobAzDE6RqqnVXbo6Z/cLMdpjZ783sTTP7fblfKpIIzcOrGVH7mP4VOMXdR7r7vu4+wt33TTIwkdj6Og8vgoULO5+pIMmJmphedffnE41EpK+KdYbvvXdnZ3kF/M//hCLJipqYNpjZHWY2P9esm2NmcxKNTCSuws5wszBI88wzdYeun4mamPYFdgF/CczKlZOTCkqkbB3z8FatCkMN3n+/8w7d2WfD6NEaStAP6K6c1KZSd+jymYWk1dgYmnsR5tdpad1o+npXLtLjm8xsCHAOMBUY0rHf3f+m3C8WSVSUO3Ed/1OO8ZTgadP6FpZEE7Uptwr4Y+B44BFgLJDpFQakzsW9Exdx8u+yZVpZoBqiJqYD3P1y4C13XwmcBPxZcmGJ9FGp6So90XinzIiamPbktm+Y2SHASOCPkglJpAIK79A1NHSfd1coQi3rM58JJbbW1tDx3nG3cPRodb73IGpiWm5mHwKWAPcAzwFfTSwqkUrIXylz+/bOeXfQfdmU/MnBPWhrCyWyjoT0mc+EOXwd2tvDPiWooqImpofd/Xfuvs7dJ7n7HwEP9nqWSJZ0JCr3MJygo4Y0dGgyq152PDwhPyEVam+v+gMV+oOoiemuIvtWVzIQkapqbg534y64INSe5iQwXrjYwxOK0QM/u+kxMZnZQWb2aWBk/ohvM1tA3rABkX5rzpyQGArXG++r1tbex1HlU8d7F73VmA4kjPAeReeI71nAdODcRCPLMbNJZnaLmamGJpX3iU+E/qXm5kgjwo86KpQeXXhhmAYTh1bd7Mrdey3AUVGOK3LeCuA14JmC/ScAm4DNwKURP2t11O+dMWOGi0Ry223uAwe6h56nUIYNC/vL+ayGhq6fFaWU+30ZBmzwMnJGR4nax3S+mY3qeJF7SsqKCOe15JLQB8xsIPAt4ERgCjDfzKaY2Z+a2b0FRUMSJFmLF8N773XdV06fT5SObuh8YmapVTkFiDglBTjUC56SYmaH93aSu68zswkFu48ENrv7FgAzux2Y7e5X0YeJwWa2EFgIMF7VYokq5uJyn/502N5VeDsoSkd3Y2PXZYGlpKg1pgG5cUwAmNmHiZ7UCo0B8p/V05bbV5SZNZjZDcDhZnZZqePcfbm7N7l703777VdmaFJ3Yi4u195eolLUW+e1WUXXhap1UZPLNcATZvY9wIC5hIcTJM7d24Hzq/FdUoeWLg1NsPzaTsTBll2MH1/6LpwZnH++akkxREpM7n6rmW0A/iK3a467P1fmd74MjMt7PTa3T6T6OpLF4sWdiSW/jylKMmlthd+XWAK/oQH+7d+UlGKKuuzJeGAnYTrKB/vcvZzBF+uByWY2kZCQTgfOKONzRCqjI2mcey68/Xb4OcpSKK2tcMklxdt2Skh9ErUp9yOgY0W5ocBEwu3+qT2dZGbfBY4BRptZG/Ald7/FzC4CHgAGAivc/dkyYi/2fbOAWQcccEAlPk7qyeLFnUmpQ0fNKS+5fPKTuR867sKV6vDeZx8lpT4oawVLM5sOXOjun618SH2nFSwltgEDOheOy2cWJgEX6m2FzFLn1YmqPFeukLv/DK3HJLUk7qOfersLpyErfRK1j+nzeS8HEKak/DqRiETSUOzu3NChMHNmqB29+CKMH8+JIx+Hj3yE+3u6C1fOXT3pImqNaURe2ZvQ5zQ7qaBEqq5wYTmAww6DlStDAso9aeXtZzbz9tZXQ+IZOLD75zQ0aCR3BegpKSLFTJ4Mmzd3230MP4G9h7B2ZxOMHBmS2K5doekW8Ukr9SDRp6SY2Ro678Z14+6nlPvFSdBdOamI1tae+5D+sBvGjg0JafRouPFGJaQK660pdzVh1PevgLeBm3JlJ/DLZEOLz93XuPvCkSNHph2K9GeLF8M77/R8zKuvhu327VqBMgE91pjc/REAM7umoFq2JjcSXKT29FBbOrnLkL6cIuOdpG+iDrAcbmaT8lYEmAgMTy4skRT1cMftC1xd/BytQFlRUe/K/R9grZmtNbNHgJ8AixKLSiRNxZ5JN2hQz+do3FJFRZ3E+2MzmwwclNv1grv/IbmwRFKUP7E3N36JnTuhvT3clQPWcmzn8Rq3VHFx1lSaAUzInXOYmeHutyYSVZl0V04qprm5a5/RgB4aFxq3VHGRmnJmtopwh+7jwBG5UvYYhaTorpwkplRTLX9VSqmYqDWmJmCK1+JoTJEoPpiykrdPTbjERE1MzwB/DLySYCwi2dVRKzpnSBhg2diokd4JipqYRgPPmdmTwAed3lkb+S2SqOZmTtuR+/nCrWlGUvOiJqYvJxmESH9x4YVpR1Afog4XeMTM9id0egM86e6vJReWSDZ1rIpSOMxJKivqXbnTgCeB/w2cBvzUzOYmGVg5zGyWmS3fsWNH7weLlGHmzFAkWVFHfi8GjnD3s9z9rwkPrbw8ubDKo+ECIrUh8gMvC5pu7THOFRGJJWrn94/N7AHgu7nX84D7kglJROpdbwvFHQDs7+5/b2ZzCCO/AZ4AtACNiCSitxrTMuAyAHe/G7gbwMz+NPferARjE8mcBQvSjqA+9JaY9nf3/y7c6e7/bWYTkglJJLuUmKqjtw7sUT28N7SCcYj0C9u3hyLJ6i0xbTCzcwt3mtlngY3JhCSSXXPnhiLJ6q0ptwj4vpk105mImoDBwKkJxlUWrcckUht6rDG5+6vufjTwT8DWXPkndz/K3X+TfHjxaIClSG2IOlfuJ5BbU1REJGEavS0imRNnzW+RunfBBWlHUB+UmERimDcv7Qjqg5pyIjG89FIokizVmERiOPPMsF27NtUwap5qTCKSOUpMIpI5Skwikjk1lZi05rdIbaipzm93XwOsaWpq6jbxWKQS/u7v0o6gPtRUYhJJ2iwtjVgVNdWUE0napk2hSLJUYxKJ4bzzwlbjmJKlGpOIZI4Sk4hkjhKTiGSOEpOIZI46v0ViWLIk7QjqgxKTSAzHHZd2BPVBTTmRGJ5+OhRJlmpMIjEsWhS2GseUrJqqMWkSr0htqKnEpOfKidSGmkpMIlIblJhEJHPU+S0Sw5VXph1BfVBiEonh6KPTjqA+qCknEsPjj4ciyVKNSSSGL34xbDWOKVmqMYlI5igxiUjmKDGJSOYoMYlI5qjzWySGZcvSjqA+KDGJxDBtWtoR1Ac15URieOihUCRZqjGJxHDFFWGrlSyTpRqTiGSOEpOIZI4Sk4hkTk0lJi2tK1IbzN3TjqHimpqafMOGDWmHITVo06awPfDAdOPIOjPb6O5N5Z6vu3IiMSghVUdNNeVEkrZmTSiSLNWYRGK45pqwnTUr3ThqnWpMIpI5SkwikjlKTCKSOUpMIpI56vwWiWHVqrQjqA9KTCIxjBuXdgT1QU05kRjuuCMUSZZqTCIxXH992M6bl24ctU41JhHJHCUmEckcJSYRyRwlJhHJHHV+i8SwenXaEdQHJSaRGEaPTjuC+qCmnEgMLS2hSLKUmERiUGKqDiUmEckcJSYRyRwlJhHJHCUmEckcDRcQieG++9KOoD4oMYnEMGxY2hHUBzXlRGK47rpQJFlKTCIx3HlnKJIsJSYRyZzM9zGZ2V8BJwH7Are4+4PpRiQiSUu0xmRmK8zsNTN7pmD/CWa2ycw2m9mlPX2Gu//A3c8Fzge0oKlIHUi6xtQCfBO4tWOHmQ0EvgV8CmgD1pvZPcBA4KqC8//G3V/L/bwkd56I1LhEE5O7rzOzCQW7jwQ2u/sWADO7HZjt7lcBJxd+hpkZ8C/A/e7+s1LfZWYLgYW5lzvNbFPu55HAjoLDRwPbY/46lVYsrmp+Vpxzeju23Pfj7E/7mnWJyaxyn5XQeX25ZnHfK7bvwN4C7JG7J1qACcAzea/nAjfnvT4T+GYP518MbARuAM4v4/uXF9m3Ienfu5y4qvlZcc7p7dhy34+zP+1rlvb1quY1i/teEtcr853f7v514Ot9+Ig1lYqlwioZVzmfFeec3o4t9/24+9OU9vWKe15frlnc9yp+vSyX3RKTa8rd6+6H5F4fBXzZ3Y/Pvb4MwENTrirMbIO7N1Xr+6TvdM36l75erzTGMa0HJpvZRDMbDJwO3FPlGJZX+fuk73TN+pc+Xa9Ea0xm9l3gGELH5avAl9z9FjObCSwj3Ilb4e5LEwtCRPqdxJtyIiJxaUqKiGSOEpOIZE7dJyYzG25mK83sJjNrTjse6Z2ZTTKzW8xMj5/sJ8zsr3J/Y3eY2V/2dnxNJqaYc/TmAKs9zMc7perBChDvmrn7Fnc/J51IpUPMa/YDjzHntSYTE2GO3gn5O/Lm6J0ITAHmm9kUYCzwUu6w96oYo3TVQvRrJtnQQvxrFmnOa00mJndfB/y2YPcHc/Tc/R3gdmA2YSLx2NwxNfnfoz+Iec0kA+JcMwu+Si9zXjvU0x/iGDprRhAS0hjgbuDTZnY92ZwKUc+KXjMzazCzG4DDO2YOSGaU+jv7HHAcMNfMzu/tQzI/Vy5p7v4WcHbacUh07t5O6KuQfiLunNd6qjG9DIzLez02t0+yS9es/6nINaunxJSFOXoSj65Z/1ORa1aTiSk3R+8J4EAzazOzc9z9XeAi4AHgeeBOd382zTilk65Z/5PkNdNcORHJnJqsMYlI/6bEJCKZo8QkIpmjxCQimaPEJCKZo8QkIpmjxCSZYWYTCpfQkPqkxCQimaPEJJmUW6XyKTM7Iu1YpPrqfnUByR4zO5Cwjs8Cd/+vtOOR6lNikqzZD/ghMMfdn0s7GEmHmnKSNTuAF4GPpx2IpEc1Jsmad4BTgQfMbKe7fyftgKT6lJgkc9z9LTM7Gfj3XHLSGkx1RsueiEjmqI9JRDJHiUlEMkeJSUQyR4lJRDJHiUlEMkeJSUQyR4lJRDJHiUlEMuf/A6TOsOTlpvJ1AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_min_envelope(phi_by_k, name='dolphins')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}