centrality.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "All-subgraphs.ipynb",
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AliAkbarBadri/graph-centrality/blob/main/centrality.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OZ0atjq8ITyJ"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3dvxgt-0_SLz"
      },
      "source": [
        "import networkx as nx\n",
        "import glob\n",
        "import pandas as pd\n",
        "import time\n",
        "import numpy as np\n",
        "import json\n",
        "from multiprocessing import Pool"
      ],
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LW2WBtEX7SoI"
      },
      "source": [
        "# Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BKxHr_vDBBpA"
      },
      "source": [
        "def count_subgraph(G, v):\n",
        "  neighbours = G.edges(v)\n",
        "  if len(neighbours) == 0:\n",
        "    return 1\n",
        "  else:\n",
        "    for e in neighbours:\n",
        "      G_temp = G.copy()\n",
        "      G_temp.remove_edge(*e)\n",
        "      a = count_subgraph(G_temp, v)\n",
        "      b = (2**G.number_of_edges(*e) - 1)*count_subgraph(nx.contracted_edge(G, e, self_loops=False), e[0])\n",
        "      return a + b"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KpSQpmDD67LT"
      },
      "source": [
        "def count_tree(T, v):\n",
        "  # print(T.edges(v))\n",
        "  # print(\"a\")\n",
        "  neighbours = T.edges(v)\n",
        "  # print(v, neighbours)\n",
        "  if len(neighbours) == 0: \n",
        "    return 1\n",
        "  else:\n",
        "    for e in neighbours:\n",
        "      T_temp = T.copy()\n",
        "      T_temp.remove_edge(*e)\n",
        "      return count_tree(T_temp, v) * (count_tree(T_temp,e[1]) + 1) "
      ],
      "execution_count": 97,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HAgBJZtBE3oS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ac101f2-df16-40fa-d6fc-e17b97ef9433"
      },
      "source": [
        "line = nx.path_graph(4)\n",
        "print(line.edges())\n",
        "\n",
        "# result must be equal to 4\n",
        "print(count_subgraph(line,0))\n",
        "print(count_tree(line, 0))"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[(0, 1), (1, 2), (2, 3)]\n",
            "4\n",
            "4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0LTsejaQPnhC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "385cc48f-7166-4d0b-db90-70dd39e2dfda"
      },
      "source": [
        "star = nx.star_graph(4)\n",
        "print(star.edges())\n",
        "# result must be equal to 16\n",
        "print(count_subgraph(star,0))\n",
        "print(count_tree(star, 0))"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[(0, 1), (0, 2), (0, 3), (0, 4)]\n",
            "16\n",
            "16\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kG9_dkdU7yb7"
      },
      "source": [
        "# Get Datasets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BP4oyxEcBR94",
        "outputId": "7026e4d3-8c18-4f82-c258-79c72f8ce821"
      },
      "source": [
        "! curl -L https://api.github.com/repos/AliAkbarBadri/graph-centrality/tarball --output repo.tar\n",
        "! tar xf repo.tar --wildcards \"*/data/*.csv\" --strip-components=1\n",
        "! rm -rf repo.tar"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
            "                                 Dload  Upload   Total   Spent    Left  Speed\n",
            "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0\n",
            "100  440k    0  440k    0     0   977k      0 --:--:-- --:--:-- --:--:--  977k\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "--ftsNNbGF8l",
        "outputId": "3130f8f5-3d34-4e55-a639-77d41cbccf0a"
      },
      "source": [
        "for file_name in sorted(glob.glob('data/*.csv')):\n",
        "  print(file_name.split(\"/\")[1].split(\".csv\")[0])"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ENZYMES_g297\n",
            "aves-songbird-social\n",
            "bn-mouse_visual-cortex_1\n",
            "bn-mouse_visual-cortex_2\n",
            "ca-sandi_auths\n",
            "email-dnc-corecipient\n",
            "email-enron-only\n",
            "facebook-socfb-Amherst41\n",
            "insecta-ant-colony1-day01\n",
            "reptilia-tortoise-network-lm\n",
            "road-chesapeake\n",
            "rt-retweet\n",
            "soc-dolphins\n",
            "soc-wiki-Vote\n",
            "web-edu\n",
            "web-polblogs\n",
            "web-spam\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHxd_SiIGytl"
      },
      "source": [
        "# Test on datasets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nw_iWAW_HQ9S"
      },
      "source": [
        "def create_graph_from_csv(dir_name:str) -> dict:\n",
        "  graphs = {}\n",
        "  for file_name in sorted(glob.glob(dir_name+'/*.csv')):\n",
        "    df = pd.read_csv(file_name,header=None,names=['src', 'dest'])\n",
        "    G = nx.from_pandas_edgelist(df,source=\"src\",target=\"dest\", create_using=nx.DiGraph())\n",
        "    dataset_name = file_name.split(\"/\")[1].split(\".csv\")[0]\n",
        "    print(dataset_name, G.number_of_nodes(), G.number_of_edges())\n",
        "    graphs[dataset_name] = G\n",
        "  return graphs"
      ],
      "execution_count": 110,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "48SbHIHeHbAw",
        "outputId": "87ff190c-779d-4d8f-fc6a-5b2884f743ea"
      },
      "source": [
        "graphs = create_graph_from_csv(dir_name= \"data\")"
      ],
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ENZYMES_g297 121 298\n",
            "aves-songbird-social 110 1027\n",
            "bn-mouse_visual-cortex_1 29 44\n",
            "bn-mouse_visual-cortex_2 193 214\n",
            "ca-sandi_auths 86 124\n",
            "email-dnc-corecipient 906 12085\n",
            "email-enron-only 143 623\n",
            "facebook-socfb-Amherst41 2235 90953\n",
            "insecta-ant-colony1-day01 113 4550\n",
            "reptilia-tortoise-network-lm 45 106\n",
            "road-chesapeake 39 170\n",
            "rt-retweet 96 117\n",
            "soc-dolphins 62 159\n",
            "soc-wiki-Vote 889 2914\n",
            "web-edu 3031 6474\n",
            "web-polblogs 643 2280\n",
            "web-spam 4767 37375\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "huq3XtzW6j1C"
      },
      "source": [
        "graph_names = [\n",
        "               \"bn-mouse_visual-cortex_1\",\n",
        "               \"ca-sandi_auths\",\n",
        "               \"reptilia-tortoise-network-lm\",\n",
        "               \"road-chesapeake\",\n",
        "               \"rt-retweet\"\n",
        "               ]"
      ],
      "execution_count": 112,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z7NLuGtu0Cta"
      },
      "source": [
        "# Tree Centrality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gCWZEZRrCqFi"
      },
      "source": [
        "tree_centrality = {}\n",
        "tree_time = {}"
      ],
      "execution_count": 118,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "722Kg4rro7H6",
        "outputId": "76dba012-9d23-42ac-b3cc-9bfced23f5c2"
      },
      "source": [
        "for key in graph_names:\n",
        "  print(\"Graph:\",key)\n",
        "  tree_centrality[key] = {}\n",
        "  G = graphs[key]\n",
        "  start_time_all = time.time()\n",
        "  for node in G.nodes():\n",
        "    # print(node,\"-\")\n",
        "    c = count_tree(G, node)\n",
        "    # print(node, c)\n",
        "    tree_centrality[key][node] = c\n",
        "  all_time = time.time() - start_time_all\n",
        "  print(\" time:\", all_time)\n",
        "  tree_time[key] = all_time"
      ],
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Graph: bn-mouse_visual-cortex_1\n",
            " time: 0.013124704360961914\n",
            "Graph: ca-sandi_auths\n",
            " time: 0.25470709800720215\n",
            "Graph: reptilia-tortoise-network-lm\n",
            " time: 1.0627782344818115\n",
            "Graph: road-chesapeake\n",
            " time: 1.2863714694976807\n",
            "Graph: rt-retweet\n",
            " time: 0.18354249000549316\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8ah0XVFpERlN"
      },
      "source": [
        "with open('results/tree_centrality.json', 'w') as fp:\n",
        "    json.dump(tree_centrality, fp, indent=4)\n",
        "with open('results/tree_time.json', 'w') as fp:\n",
        "    json.dump(tree_time, fp, indent=4)"
      ],
      "execution_count": 120,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yUHqtnpwEprH"
      },
      "source": [
        "# Graph Centrality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BTO3WdPUE0OQ"
      },
      "source": [
        "graph_centrality = {}\n",
        "graph_time = {}"
      ],
      "execution_count": 122,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uirMOCu-189h"
      },
      "source": [
        "def fun(G, v):\n",
        "    # print(v,\"-\")\n",
        "    centrality = count_subgraph(G,v)\n",
        "    print('\"{0}\": {1},'.format(v,centrality))\n",
        "    return (v,centrality)"
      ],
      "execution_count": 137,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F6Wf8U4D12YR",
        "outputId": "a079b062-eeee-4dfe-da55-9516158f78a5"
      },
      "source": [
        "for key in graph_names:\n",
        "    print(\"Graph:\",key)\n",
        "    graph_centrality[key] = {}\n",
        "    G = graphs[key]\n",
        "    start_time_all = time.time()\n",
        "    with Pool(processes=4) as pool:\n",
        "        graph_centrality[key] = pool.starmap(fun, zip([G]*G.number_of_nodes(), list(G.nodes())))\n",
        "    all_time = time.time() - start_time_all\n",
        "    print(\" time:\", all_time)\n",
        "    print()\n",
        "    graph_time[key] = all_time"
      ],
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Graph: bn-mouse_visual-cortex_1\n",
            "\"1\": 2,\n",
            "\"18\": 1,\n",
            "\"19\": 1,\n",
            "\"28\": 1,\n",
            "\"20\": 1,\n",
            "\"14\": 1,\n",
            "\"16\": 1,\n",
            "\"3\": 8,\n",
            "\"21\": 1,\n",
            "\"13\": 1,\n",
            "\"15\": 1,\n",
            "\"6\": 2,\n",
            "\"22\": 1,\n",
            "\"8\": 2,\n",
            "\"5\": 48,\n",
            "\"2\": 64,\n",
            "\"17\": 1,\n",
            "\"23\": 1,\n",
            "\"25\": 1,\n",
            "\"24\": 1,\n",
            "\"26\": 1,\n",
            "\"7\": 72,\n",
            "\"4\": 1,\n",
            "\"10\": 64,\n",
            "\"27\": 1,\n",
            "\"11\": 8,\n",
            "\"12\": 32,\n",
            "\"9\": 512,\n",
            "\"0\": 1,\n",
            " time: 0.44628357887268066\n",
            "\n",
            "Graph: ca-sandi_auths\n",
            "\"35\": 2,\n",
            "\"1\": 1,\n",
            "\"32\": 5,\n",
            "\"10\": 2,\n",
            "\"16\": 2,\n",
            "\"37\": 5,\n",
            "\"18\": 2,\n",
            "\"33\": 20,\n",
            "\"67\": 5,\n",
            "\"2\": 1,\n",
            "\"75\": 2,\n",
            "\"26\": 2,\n",
            "\"5\": 1,\n",
            "\"30\": 20,\n",
            "\"60\": 16,\n",
            "\"15\": 2,\n",
            "\"6\": 1,\n",
            "\"66\": 75,\n",
            "\"40\": 80,\n",
            "\"76\": 200,\n",
            "\"7\": 2,\n",
            "\"3\": 1,\n",
            "\"20\": 2,\n",
            "\"8\": 1,\n",
            "\"64\": 5,\n",
            "\"23\": 2,\n",
            "\"9\": 1,\n",
            "\"46\": 2,\n",
            "\"11\": 1,\n",
            "\"12\": 1,\n",
            "\"36\": 837,\n",
            "\"65\": 2,\n",
            "\"25\": 2,\n",
            "\"17\": 1,\n",
            "\"31\": 2,\n",
            "\"84\": 738,\n",
            "\"19\": 1,\n",
            "\"22\": 3,\n",
            "\"56\": 3,\n",
            "\"81\": 6,\n",
            "\"21\": 1,\n",
            "\"44\": 2337,\n",
            "\"52\": 2,\n",
            "\"57\": 2,\n",
            "\"54\": 162,\n",
            "\"86\": 31,\n",
            "\"27\": 1,\n",
            "\"41\": 32,\n",
            "\"48\": 105,\n",
            "\"28\": 1,\n",
            "\"55\": 32,\n",
            "\"74\": 10,\n",
            "\"29\": 1,\n",
            "\"61\": 105,\n",
            "\"62\": 21,\n",
            "\"82\": 21,\n",
            "\"83\": 62,\n",
            "\"34\": 21,\n",
            "\"80\": 3278,\n",
            "\"43\": 1398,\n",
            "\"24\": 1,\n",
            "\"68\": 838,\n",
            "\"73\": 4291,\n",
            "\"85\": 838,\n",
            "\"39\": 2,\n",
            "\"38\": 1,\n",
            "\"45\": 81,\n",
            "\"53\": 13990,\n",
            "\"4\": 1,\n",
            "\"49\": 4,\n",
            "\"78\": 6,\n",
            "\"70\": 1,\n",
            "\"69\": 29369,\n",
            "\"72\": 29369,\n",
            "\"58\": 167706,\n",
            "\"77\": 84,\n",
            "\"71\": 3,\n",
            "\"42\": 838,\n",
            "\"79\": 102086,\n",
            "\"47\": 1,\n",
            "\"50\": 1,\n",
            "\"63\": 1,\n",
            " time: 856.629058599472\n",
            "\n",
            "Graph: reptilia-tortoise-network-lm\n",
            "\"7\": 1,\n",
            "\"10\": 4,\n",
            "\"4\": 2,\n",
            "\"5\": 1,\n",
            "\"6\": 22,\n",
            "\"13\": 56,\n",
            "\"14\": 5,\n",
            "\"11\": 200,\n",
            "\"12\": 186,\n",
            "\"1\": 1248,\n",
            "\"8\": 1246,\n",
            "\"9\": 6,\n",
            "\"2\": 1247,\n",
            "\"3\": 4,\n",
            "\"22\": 1,\n",
            "\"23\": 8,\n",
            "\"24\": 22,\n",
            "\"25\": 1,\n",
            "\"26\": 14,\n",
            "\"19\": 2090,\n",
            "\"20\": 1420,\n",
            "\"27\": 4552,\n",
            "\"28\": 2,\n",
            "\"29\": 147,\n",
            "\"30\": 2,\n",
            "\"31\": 1247,\n",
            "\"32\": 162,\n",
            "\"33\": 36,\n",
            "\"21\": 7817,\n",
            "\"37\": 7,\n",
            "\"38\": 4,\n",
            "\"39\": 2,\n",
            "\"40\": 7,\n",
            "\"41\": 2,\n",
            "\"42\": 11,\n",
            "\"43\": 3,\n",
            "\"44\": 1,\n",
            "\"34\": 4587,\n",
            "\"35\": 10,\n",
            "\"36\": 8,\n",
            "\"45\": 3396,\n",
            "\"16\": 1039607,\n",
            "\"17\": 24485,\n",
            "\"18\": 4264,\n",
            "\"15\": 4036344,\n",
            " time: 1614.1442775726318\n",
            "\n",
            "Graph: road-chesapeake\n",
            "\"7\": 12,\n",
            "\"1\": 1,\n",
            "\"8\": 31,\n",
            "\"11\": 31,\n",
            "\"12\": 31,\n",
            "\"13\": 31,\n",
            "\"22\": 61,\n",
            "\"23\": 61,\n",
            "\"34\": 4,\n",
            "\"35\": 160581,\n",
            "\"37\": 820348,\n",
            "\"39\": 2341044,\n",
            "\"2\": 1,\n",
            "\"9\": 80,\n",
            "\"36\": 3381492,\n",
            "\"14\": 2,\n",
            "\"3\": 1,\n",
            "\"15\": 2,\n",
            "\"16\": 2,\n",
            "\"17\": 4,\n",
            "\"18\": 2,\n",
            "\"4\": 1,\n",
            "\"6\": 2,\n",
            "\"5\": 1,\n",
            "\"10\": 143,\n",
            "\"20\": 32,\n",
            "\"21\": 32,\n",
            "\"24\": 32,\n",
            "\"38\": 920126,\n",
            "\"19\": 1410,\n",
            "\"26\": 480,\n",
            "\"25\": 15,\n",
            "\"27\": 1922,\n",
            "\"28\": 434,\n",
            "\"29\": 15,\n",
            "\"32\": 1758,\n",
            "\"33\": 26736,\n",
            "\"30\": 12646,\n",
            "\"31\": 62,\n",
            " time: 17560.795307652936302\n",
            "\n",
            "Graph: rt-retweet\n",
            "\"6\": 2,\n",
            "\"1\": 1,\n",
            "\"8\": 5,\n",
            "\"54\": 23616,\n",
            "\"76\": 2,\n",
            "\"85\": 2,\n",
            "\"56\": 888,\n",
            "\"2\": 1,\n",
            "\"75\": 784,\n",
            "\"3\": 1,\n",
            "\"19\": 2,\n",
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            "\"72\": 952414,\n",
            "\"9\": 1,\n",
            "\"95\": 34170,\n",
            "\"10\": 1,\n",
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            "\"94\": 2,\n",
            "\"15\": 2,\n",
            "\"12\": 1,\n",
            "\"24\": 2,\n",
            "\"13\": 1,\n",
            "\"41\": 2,\n",
            "\"14\": 1,\n",
            "\"50\": 14,\n",
            "\"21\": 3,\n",
            "\"33\": 3,\n",
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            "\"68\": 4,\n",
            "\"51\": 2,\n",
            "\"23\": 1,\n",
            "\"25\": 1,\n",
            "\"26\": 1,\n",
            "\"27\": 1,\n",
            "\"32\": 13,\n",
            "\"78\": 13,\n",
            "\"29\": 1,\n",
            "\"64\": 10,\n",
            "\"30\": 1,\n",
            "\"31\": 1,\n",
            "\"55\": 2,\n",
            "\"58\": 74,\n",
            "\"34\": 1,\n",
            "\"35\": 1,\n",
            "\"36\": 1,\n",
            "\"37\": 1,\n",
            "\"59\": 3,\n",
            "\"66\": 3,\n",
            "\"81\": 33,\n",
            "\"88\": 3,\n",
            "\"43\": 1,\n",
            "\"74\": 444,\n",
            "\"44\": 1,\n",
            "\"79\": 98,\n",
            "\"83\": 49,\n",
            "\"46\": 1,\n",
            "\"47\": 1,\n",
            "\"73\": 2,\n",
            "\"48\": 1,\n",
            "\"87\": 2,\n",
            "\"70\": 10,\n",
            "\"49\": 1,\n",
            "\"77\": 15,\n",
            "\"52\": 1,\n",
            "\"57\": 5,\n",
            "\"67\": 23617,\n",
            "\"92\": 23617,\n",
            "\"80\": 889,\n",
            "\"90\": 889,\n",
            "\"60\": 1,\n",
            "\"62\": 1,\n",
            "\"63\": 1,\n",
            "\"91\": 3,\n",
            "\"69\": 1,\n",
            "\"71\": 1,\n",
            "\"82\": 1,\n",
            "\"86\": 1,\n",
            " time: 13916.38764382746283\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o2crzdJAFE-i"
      },
      "source": [
        "# Betweenness Centrality\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZkwzKn_Mg1ZF"
      },
      "source": [
        "betweenness_centrality = {}"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1BDoAcOGKQF-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "929b3eb3-4638-4f77-8503-668a16ecb345"
      },
      "source": [
        "for key in graph_names:\n",
        "  print(\"Graph:\",key)\n",
        "  G = graphs[key]\n",
        "  betweenness_centrality[key] = nx.betweenness_centrality(G)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Graph: ca-sandi_auths\n",
            "Graph: reptilia-tortoise-network-lm\n",
            "Graph: bn-mouse_visual-cortex_1\n",
            "Graph: road-chesapeake\n",
            "Graph: rt-retweet\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_dcJJrLRMr6K"
      },
      "source": [
        "with open('results/betweenness_centrality.json', 'w') as fp:\n",
        "    json.dump(betweenness_centrality, fp, indent=4)"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dMwgJJvSiHiJ",
        "outputId": "8f089ec2-df86-447d-ded3-25a90dd346c2"
      },
      "source": [
        "betweenness_centrality"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              " 'reptilia-tortoise-network-lm': {1: 0.0007047216349541931,\n",
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              " 'road-chesapeake': {1: 0.0,\n",
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              "  39: 0.0},\n",
              " 'rt-retweet': {1: 0.0,\n",
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              "  96: 0.0}}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4rxj8D5EKQkM"
      },
      "source": [
        "# Eigenvector Centrality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ofNpZxzrFJlq"
      },
      "source": [
        "eigenvector_centrality = {}"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UrwrTXtMhYpZ",
        "outputId": "64486a17-77b9-4207-c73c-28187b1f7121"
      },
      "source": [
        "for key in graph_names:\n",
        "  print(\"Graph:\",key)\n",
        "  G = graphs[key]\n",
        "  eigenvector_centrality[key] = nx.eigenvector_centrality(G, max_iter=1000)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Graph: ca-sandi_auths\n",
            "Graph: reptilia-tortoise-network-lm\n",
            "Graph: bn-mouse_visual-cortex_1\n",
            "Graph: road-chesapeake\n",
            "Graph: rt-retweet\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z4PpdEnqKMj-"
      },
      "source": [
        "with open('results/eigenvector_centrality.json', 'w') as fp:\n",
        "    json.dump(eigenvector_centrality, fp, indent=4)"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q4zi5bXUiFVR",
        "outputId": "053bcd6c-65bb-4ac2-b2b3-13e8a45294df"
      },
      "source": [
        "eigenvector_centrality"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  43: 2.5305549529055853e-09,\n",
              "  44: 5.254004085274772e-14,\n",
              "  45: 9.96291826885388e-12,\n",
              "  46: 2.5205658167049112e-09,\n",
              "  47: 1.984704383929734e-11,\n",
              "  48: 3.4725737510077855e-17,\n",
              "  49: 5.254004085274772e-14,\n",
              "  50: 2.628738329512899e-14,\n",
              "  51: 3.4725737510077855e-17,\n",
              "  52: 3.4725737510077855e-17,\n",
              "  53: 9.989170926411486e-12,\n",
              "  54: 3.4725737510077855e-17,\n",
              "  55: 9.96291826885388e-12,\n",
              "  56: 3.4725737510077855e-17,\n",
              "  57: 3.4725737510077855e-17,\n",
              "  58: 2.628738329512899e-14,\n",
              "  59: 3.4725737510077855e-17,\n",
              "  60: 3.4725737510077855e-17,\n",
              "  61: 3.4725737510077855e-17,\n",
              "  62: 3.4725737510077855e-17,\n",
              "  63: 2.628738329512899e-14,\n",
              "  64: 2.628738329512899e-14,\n",
              "  65: 2.628738329512899e-14,\n",
              "  66: 2.628738329512899e-14,\n",
              "  67: 3.4725737510077855e-17,\n",
              "  68: 3.4725737510077855e-17,\n",
              "  69: 3.4725737510077855e-17,\n",
              "  70: 2.628738329512899e-14,\n",
              "  71: 3.4725737510077855e-17,\n",
              "  72: 2.628738329512899e-14,\n",
              "  73: 3.4725737510077855e-17,\n",
              "  74: 3.4725737510077855e-17,\n",
              "  75: 3.4725737510077855e-17,\n",
              "  76: 3.4725737510077855e-17,\n",
              "  77: 3.4725737510077855e-17,\n",
              "  78: 3.4725737510077855e-17,\n",
              "  79: 3.4725737510077855e-17,\n",
              "  80: 3.4725737510077855e-17,\n",
              "  81: 3.4725737510077855e-17,\n",
              "  82: 9.936665611296257e-12,\n",
              "  83: 2.628738329512899e-14,\n",
              "  84: 3.4725737510077855e-17,\n",
              "  85: 3.4725737510077855e-17,\n",
              "  86: 3.4725737510077855e-17},\n",
              " 'reptilia-tortoise-network-lm': {1: 2.5943125782280243e-21,\n",
              "  2: 7.666237491511416e-19,\n",
              "  3: 2.5943125782280243e-21,\n",
              "  4: 7.692136794446093e-19,\n",
              "  5: 1.5230430853003269e-16,\n",
              "  6: 4.382284760520311e-24,\n",
              "  7: 0.7005726172531864,\n",
              "  8: 5.3114550815534665e-12,\n",
              "  9: 0.00021914592027424718,\n",
              "  10: 0.013104032205606575,\n",
              "  11: 5.267565250058585e-10,\n",
              "  12: 4.382284760520311e-24,\n",
              "  13: 2.5943125782280243e-21,\n",
              "  14: 5.214452222389738e-10,\n",
              "  15: 4.382284760520311e-24,\n",
              "  16: 2.5943125782280243e-21,\n",
              "  17: 7.692136794446093e-19,\n",
              "  18: 1.5230171859973922e-16,\n",
              "  19: 1.5154545895404666e-16,\n",
              "  20: 4.4857451967693504e-14,\n",
              "  21: 7.666237491511416e-19,\n",
              "  22: 0.7134607180738284,\n",
              "  23: 1.5153509923287287e-16,\n",
              "  24: 3.3031858779671904e-06,\n",
              "  25: 0.00021914539621883602,\n",
              "  26: 4.382284760520311e-24,\n",
              "  27: 4.382284760520311e-24,\n",
              "  28: 2.5943125782280243e-21,\n",
              "  29: 4.382284760520311e-24,\n",
              "  30: 2.5943125782280243e-21,\n",
              "  31: 4.382284760520311e-24,\n",
              "  32: 4.382284760520311e-24,\n",
              "  33: 4.432661187418147e-08,\n",
              "  34: 4.382284760520311e-24,\n",
              "  35: 4.382284760520311e-24,\n",
              "  36: 4.382284760520311e-24,\n",
              "  37: 2.235143167470463e-14,\n",
              "  38: 4.382284760520311e-24,\n",
              "  39: 7.692136794446093e-19,\n",
              "  40: 4.382284760520311e-24,\n",
              "  41: 4.382284760520311e-24,\n",
              "  42: 4.382284760520311e-24,\n",
              "  43: 4.382284760520311e-24,\n",
              "  44: 7.692136794446093e-19,\n",
              "  45: 4.382284760520311e-24},\n",
              " 'road-chesapeake': {1: 0.009480512305996624,\n",
              "  2: 0.009480636550603196,\n",
              "  3: 1.3083700213404499e-06,\n",
              "  4: 2.689883618630238e-12,\n",
              "  5: 0.9998658841460839,\n",
              "  6: 0.009404541608452692,\n",
              "  7: 7.571624469314349e-05,\n",
              "  8: 5.046205111001182e-07,\n",
              "  9: 6.684372819524723e-10,\n",
              "  10: 2.686282709957283e-12,\n",
              "  11: 1.0006421123333957e-09,\n",
              "  12: 1.0046625268667526e-09,\n",
              "  13: 2.6898836186302387e-12,\n",
              "  14: 1.0140302907794497e-09,\n",
              "  15: 2.0119861204028935e-09,\n",
              "  16: 1.995918865904156e-09,\n",
              "  17: 7.206657276926982e-15,\n",
              "  18: 2.0119861204028935e-09,\n",
              "  19: 4.027621190633957e-12,\n",
              "  20: 1.0807565949884457e-14,\n",
              "  21: 4.027621190633957e-12,\n",
              "  22: 2.0146687973642486e-09,\n",
              "  23: 1.474032449268247e-11,\n",
              "  24: 1.0807565949884457e-14,\n",
              "  25: 1.0807565949884457e-14,\n",
              "  26: 1.0807565949884457e-14,\n",
              "  27: 4.027621190633957e-12,\n",
              "  28: 1.0807565949884457e-14,\n",
              "  29: 1.0807565949884457e-14,\n",
              "  30: 1.0807565949884457e-14,\n",
              "  31: 4.027621190633957e-12,\n",
              "  32: 1.0807565949884457e-14,\n",
              "  33: 1.0807565949884457e-14,\n",
              "  34: 3.605748603969521e-15,\n",
              "  35: 7.206657276926982e-15,\n",
              "  36: 4.839931012039615e-18,\n",
              "  37: 4.839931012039615e-18,\n",
              "  38: 4.839931012039615e-18,\n",
              "  39: 4.839931012039615e-18},\n",
              " 'rt-retweet': {1: 0.9997129751620748,\n",
              "  2: 1.2121131395338753e-07,\n",
              "  3: 8.619160513775003e-12,\n",
              "  4: 0.0004928759027017877,\n",
              "  5: 2.508116061338886e-09,\n",
              "  6: 0.023942014290547493,\n",
              "  7: 1.199787441758328e-07,\n",
              "  8: 0.0005016130165166656,\n",
              "  9: 8.613428831681498e-06,\n",
              "  10: 8.613411653008646e-06,\n",
              "  11: 8.853369081712141e-06,\n",
              "  12: 1.2121131395338753e-07,\n",
              "  13: 1.7208496942727242e-11,\n",
              "  14: 1.2245247306737116e-07,\n",
              "  15: 1.2583676109263281e-09,\n",
              "  16: 2.982408482275089e-14,\n",
              "  17: 2.982408482275089e-14,\n",
              "  18: 1.2411889380684236e-09,\n",
              "  19: 8.613411653008646e-06,\n",
              "  20: 2.982408482275089e-14,\n",
              "  21: 8.619160513775003e-12,\n",
              "  22: 2.399660478640099e-07,\n",
              "  23: 0.0005017218505670015,\n",
              "  24: 2.982408482275089e-14,\n",
              "  25: 3.7063284931777227e-09,\n",
              "  26: 8.619160513775003e-12,\n",
              "  27: 2.387162994135973e-07,\n",
              "  28: 2.579783337167951e-11,\n",
              "  29: 8.614661401459055e-06,\n",
              "  30: 2.4737587156230714e-09,\n",
              "  31: 8.732166386919264e-06,\n",
              "  32: 2.982408482275089e-14,\n",
              "  33: 2.982408482275089e-14,\n",
              "  34: 8.619160513775003e-12,\n",
              "  35: 8.732149208246412e-06,\n",
              "  36: 8.613411653008646e-06,\n",
              "  37: 8.613411653008646e-06,\n",
              "  38: 8.613411653008646e-06,\n",
              "  39: 1.2411889380684236e-09,\n",
              "  40: 1.7208496942727242e-11,\n",
              "  41: 1.2583676109263281e-09,\n",
              "  42: 2.982408482275089e-14,\n",
              "  43: 8.732157797582837e-06,\n",
              "  44: 1.2411889380684236e-09,\n",
              "  45: 1.212542606355321e-07,\n",
              "  46: 8.619160513775003e-12,\n",
              "  47: 8.613411653008646e-06,\n",
              "  48: 2.579783337167951e-11,\n",
              "  49: 8.619160513775003e-12,\n",
              "  50: 8.619160513775003e-12,\n",
              "  51: 8.735872685588365e-06,\n",
              "  52: 1.2121131395338753e-07,\n",
              "  53: 2.4909373884809794e-09,\n",
              "  54: 1.200131015215485e-07,\n",
              "  55: 2.982408482275089e-14,\n",
              "  56: 1.2583676109263281e-09,\n",
              "  57: 2.982408482275089e-14,\n",
              "  58: 2.982408482275089e-14,\n",
              "  59: 2.982408482275089e-14,\n",
              "  60: 8.619160513775003e-12,\n",
              "  61: 1.2497782744973758e-09,\n",
              "  62: 1.2411889380684236e-09,\n",
              "  63: 8.619160513775003e-12,\n",
              "  64: 1.7208496942727242e-11,\n",
              "  65: 8.619160513775003e-12,\n",
              "  66: 8.619160513775003e-12,\n",
              "  67: 2.982408482275089e-14,\n",
              "  68: 2.982408482275089e-14,\n",
              "  69: 1.2411889380684236e-09,\n",
              "  70: 2.982408482275089e-14,\n",
              "  71: 8.619160513775003e-12,\n",
              "  72: 8.619160513775003e-12,\n",
              "  73: 2.982408482275089e-14,\n",
              "  74: 2.982408482275089e-14,\n",
              "  75: 2.982408482275089e-14,\n",
              "  76: 2.982408482275089e-14,\n",
              "  77: 2.982408482275089e-14,\n",
              "  78: 2.982408482275089e-14,\n",
              "  79: 2.982408482275089e-14,\n",
              "  80: 2.982408482275089e-14,\n",
              "  81: 2.982408482275089e-14,\n",
              "  82: 8.619160513775003e-12,\n",
              "  83: 2.982408482275089e-14,\n",
              "  84: 8.619160513775003e-12,\n",
              "  85: 2.982408482275089e-14,\n",
              "  86: 8.619160513775003e-12,\n",
              "  87: 2.982408482275089e-14,\n",
              "  88: 2.982408482275089e-14,\n",
              "  89: 2.982408482275089e-14,\n",
              "  90: 2.982408482275089e-14,\n",
              "  91: 2.982408482275089e-14,\n",
              "  92: 2.982408482275089e-14,\n",
              "  93: 2.982408482275089e-14,\n",
              "  94: 2.982408482275089e-14,\n",
              "  95: 2.982408482275089e-14,\n",
              "  96: 2.982408482275089e-14}}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_FNwuzBGM92Z"
      },
      "source": [
        "# Degree Centrality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b6kYEKjOMfsw"
      },
      "source": [
        "degree_centrality = {}"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "csew9JwNhh6j",
        "outputId": "527264e3-18ad-4d3c-f5d5-b3cfd14e52fb"
      },
      "source": [
        "for key in graph_names:\n",
        "  print(\"Graph:\",key)\n",
        "  G = graphs[key]\n",
        "  degree_centrality[key] = nx.degree_centrality(G)"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Graph: ca-sandi_auths\n",
            "Graph: reptilia-tortoise-network-lm\n",
            "Graph: bn-mouse_visual-cortex_1\n",
            "Graph: road-chesapeake\n",
            "Graph: rt-retweet\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gH7AI54ANHgq"
      },
      "source": [
        "with open('results/degree_centrality.json', 'w') as fp:\n",
        "    json.dump(degree_centrality, fp, indent=4)"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SB1pI1i7hq31",
        "outputId": "ab70e809-1b30-4d1b-efb5-e58593337356"
      },
      "source": [
        "degree_centrality"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'bn-mouse_visual-cortex_1': {0: 0.10714285714285714,\n",
              "  1: 0.10714285714285714,\n",
              "  2: 0.21428571428571427,\n",
              "  3: 0.14285714285714285,\n",
              "  4: 0.03571428571428571,\n",
              "  5: 0.17857142857142855,\n",
              "  6: 0.03571428571428571,\n",
              "  7: 0.14285714285714285,\n",
              "  8: 0.03571428571428571,\n",
              "  9: 0.3214285714285714,\n",
              "  10: 0.21428571428571427,\n",
              "  11: 0.10714285714285714,\n",
              "  12: 0.17857142857142855,\n",
              "  13: 0.07142857142857142,\n",
              "  14: 0.07142857142857142,\n",
              "  15: 0.07142857142857142,\n",
              "  16: 0.10714285714285714,\n",
              "  17: 0.07142857142857142,\n",
              "  18: 0.07142857142857142,\n",
              "  19: 0.07142857142857142,\n",
              "  20: 0.07142857142857142,\n",
              "  21: 0.07142857142857142,\n",
              "  22: 0.14285714285714285,\n",
              "  23: 0.07142857142857142,\n",
              "  24: 0.07142857142857142,\n",
              "  25: 0.07142857142857142,\n",
              "  26: 0.07142857142857142,\n",
              "  27: 0.07142857142857142,\n",
              "  28: 0.14285714285714285},\n",
              " 'ca-sandi_auths': {1: 0.023529411764705882,\n",
              "  2: 0.07058823529411765,\n",
              "  3: 0.11764705882352941,\n",
              "  4: 0.011764705882352941,\n",
              "  5: 0.023529411764705882,\n",
              "  6: 0.023529411764705882,\n",
              "  7: 0.023529411764705882,\n",
              "  8: 0.023529411764705882,\n",
              "  9: 0.011764705882352941,\n",
              "  10: 0.023529411764705882,\n",
              "  11: 0.023529411764705882,\n",
              "  12: 0.011764705882352941,\n",
              "  13: 0.011764705882352941,\n",
              "  14: 0.023529411764705882,\n",
              "  15: 0.023529411764705882,\n",
              "  16: 0.023529411764705882,\n",
              "  17: 0.03529411764705882,\n",
              "  18: 0.047058823529411764,\n",
              "  19: 0.011764705882352941,\n",
              "  20: 0.07058823529411765,\n",
              "  21: 0.011764705882352941,\n",
              "  22: 0.023529411764705882,\n",
              "  23: 0.03529411764705882,\n",
              "  24: 0.023529411764705882,\n",
              "  25: 0.011764705882352941,\n",
              "  26: 0.047058823529411764,\n",
              "  27: 0.03529411764705882,\n",
              "  28: 0.03529411764705882,\n",
              "  29: 0.011764705882352941,\n",
              "  30: 0.1411764705882353,\n",
              "  31: 0.023529411764705882,\n",
              "  32: 0.047058823529411764,\n",
              "  33: 0.11764705882352941,\n",
              "  34: 0.011764705882352941,\n",
              "  35: 0.047058823529411764,\n",
              "  36: 0.12941176470588234,\n",
              "  37: 0.023529411764705882,\n",
              "  38: 0.023529411764705882,\n",
              "  39: 0.023529411764705882,\n",
              "  40: 0.09411764705882353,\n",
              "  41: 0.03529411764705882,\n",
              "  42: 0.011764705882352941,\n",
              "  43: 0.07058823529411765,\n",
              "  44: 0.058823529411764705,\n",
              "  45: 0.03529411764705882,\n",
              "  46: 0.023529411764705882,\n",
              "  47: 0.011764705882352941,\n",
              "  48: 0.03529411764705882,\n",
              "  49: 0.047058823529411764,\n",
              "  50: 0.011764705882352941,\n",
              "  51: 0.011764705882352941,\n",
              "  52: 0.011764705882352941,\n",
              "  53: 0.08235294117647059,\n",
              "  54: 0.023529411764705882,\n",
              "  55: 0.047058823529411764,\n",
              "  56: 0.011764705882352941,\n",
              "  57: 0.011764705882352941,\n",
              "  58: 0.058823529411764705,\n",
              "  59: 0.047058823529411764,\n",
              "  60: 0.03529411764705882,\n",
              "  61: 0.023529411764705882,\n",
              "  62: 0.011764705882352941,\n",
              "  63: 0.011764705882352941,\n",
              "  64: 0.03529411764705882,\n",
              "  65: 0.023529411764705882,\n",
              "  66: 0.07058823529411765,\n",
              "  67: 0.023529411764705882,\n",
              "  68: 0.011764705882352941,\n",
              "  69: 0.023529411764705882,\n",
              "  70: 0.011764705882352941,\n",
              "  71: 0.011764705882352941,\n",
              "  72: 0.03529411764705882,\n",
              "  73: 0.023529411764705882,\n",
              "  74: 0.03529411764705882,\n",
              "  75: 0.011764705882352941,\n",
              "  76: 0.047058823529411764,\n",
              "  77: 0.03529411764705882,\n",
              "  78: 0.011764705882352941,\n",
              "  79: 0.03529411764705882,\n",
              "  80: 0.023529411764705882,\n",
              "  81: 0.023529411764705882,\n",
              "  82: 0.023529411764705882,\n",
              "  83: 0.03529411764705882,\n",
              "  84: 0.047058823529411764,\n",
              "  85: 0.011764705882352941,\n",
              "  86: 0.023529411764705882},\n",
              " 'reptilia-tortoise-network-lm': {1: 0.045454545454545456,\n",
              "  2: 0.045454545454545456,\n",
              "  3: 0.06818181818181818,\n",
              "  4: 0.06818181818181818,\n",
              "  5: 0.06818181818181818,\n",
              "  6: 0.06818181818181818,\n",
              "  7: 0.06818181818181818,\n",
              "  8: 0.2272727272727273,\n",
              "  9: 0.2727272727272727,\n",
              "  10: 0.2727272727272727,\n",
              "  11: 0.25,\n",
              "  12: 0.09090909090909091,\n",
              "  13: 0.11363636363636365,\n",
              "  14: 0.20454545454545456,\n",
              "  15: 0.09090909090909091,\n",
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            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    }
  ]
}