SMM_Community_Detection_prabhj.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DZuJgz7f2IZ3"
   },
   "source": [
    "## Super Mario Maker Dataset - Community Detection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ErHiyzZVVERF"
   },
   "source": [
    "### 1. Prerequisites"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "moaC0uhpU5i_"
   },
   "source": [
    "Import required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 138
    },
    "colab_type": "code",
    "id": "hthCYrf-F1bA",
    "outputId": "8ef2de4f-3a06-40ff-d795-9bd2dbddda94"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: surprise in /usr/local/lib/python3.6/dist-packages (0.1)\n",
      "Requirement already satisfied: scikit-surprise in /usr/local/lib/python3.6/dist-packages (from surprise) (1.1.0)\n",
      "Requirement already satisfied: numpy>=1.11.2 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.17.5)\n",
      "Requirement already satisfied: six>=1.10.0 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.12.0)\n",
      "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (0.14.1)\n",
      "Requirement already satisfied: scipy>=1.0.0 in /usr/local/lib/python3.6/dist-packages (from scikit-surprise->surprise) (1.4.1)\n"
     ]
    }
   ],
   "source": [
    "#!pip install surprise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CqfsTYm83mip"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, precision_recall_fscore_support\n",
    "import os\n",
    "import gc\n",
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import model_selection\n",
    "from surprise import NormalPredictor, SVD, KNNBasic, SVDpp\n",
    "from surprise import Dataset\n",
    "from surprise import Reader\n",
    "import surprise\n",
    "from surprise.model_selection import cross_validate, train_test_split\n",
    "from surprise import accuracy\n",
    "from sklearn.metrics.pairwise import cosine_similarity, cosine_distances\n",
    "import networkx as nx\n",
    "import math\n",
    "import random as rand\n",
    "import sys\n",
    "import csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pHXQkBC7U-U3"
   },
   "source": [
    "Specify data files location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6Tm0Ut1d3UY2"
   },
   "outputs": [],
   "source": [
    "data_path = '/Users/pj/Documents/671_Project/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "c-kKbKIKVr1w"
   },
   "source": [
    "Read data of games played."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UMkSzukpVrII"
   },
   "outputs": [],
   "source": [
    "plays_df = pd.read_csv(data_path + 'plays.csv', sep=\"\\t\", usecols=['id', 'player'])\n",
    "plays_df.columns = ['game', 'player']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "3Uq1p0UrVzWq",
    "outputId": "04c1b460-57b8-4ff6-b2a0-eba33b5f3f7c"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>game</th>\n",
       "      <th>player</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>darter60k</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>davidchofis</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>fabioviana</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>gorigokky</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>groebenzell</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  game       player\n",
       "0  0000-0000-0353-3D35    darter60k\n",
       "1  0000-0000-0353-3D35  davidchofis\n",
       "2  0000-0000-0353-3D35   fabioviana\n",
       "3  0000-0000-0353-3D35    gorigokky\n",
       "4  0000-0000-0353-3D35  groebenzell"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plays_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iVkjo039YmG3"
   },
   "source": [
    "Add a column with value of 0 to start with indicating game is played but not cleared by the player."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "y7LyYlsEYlR2"
   },
   "outputs": [],
   "source": [
    "plays_df['score'] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zXU4fM38V0o9"
   },
   "source": [
    "Read data of games cleared data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AGJF2Wg9V1Bb"
   },
   "outputs": [],
   "source": [
    "clears_df = pd.read_csv('/Users/pj/Documents/671_Project/clears.csv', sep='\\t', usecols=['id', 'player'])\n",
    "clears_df.columns = ['game', 'player']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "Zqz0n8RQV83l",
    "outputId": "7cdaf11c-e700-4781-9df0-797d36c36059"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>game</th>\n",
       "      <th>player</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>darter60k</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>davidchofis</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>fabioviana</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>groebenzell</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>igatake0229</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  game       player\n",
       "0  0000-0000-0353-3D35    darter60k\n",
       "1  0000-0000-0353-3D35  davidchofis\n",
       "2  0000-0000-0353-3D35   fabioviana\n",
       "3  0000-0000-0353-3D35  groebenzell\n",
       "4  0000-0000-0353-3D35  igatake0229"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clears_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DOgXluWnYvbi"
   },
   "source": [
    "Add a column with value of 1 indicating that the game is cleared by the player."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "NTL56Ih2Yv5i"
   },
   "outputs": [],
   "source": [
    "clears_df['score'] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hI4Ps_ccQGUx"
   },
   "source": [
    "Next we merge the 2 dataframes, so it now has information about games cleared as well as games played, but not cleared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ULogY0x4ZY-l"
   },
   "outputs": [],
   "source": [
    "all_data = clears_df.merge(plays_df, how='outer', on=['game', 'player'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZLbyJsRsQTSP"
   },
   "source": [
    "Replace *NaN* values with $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AgfdQWCf9WFM"
   },
   "outputs": [],
   "source": [
    "all_data.fillna(0, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LSotSseu5ALc"
   },
   "source": [
    "Drop last column *score_y* as it contains only zeroes, all required information is now available in *score_x*. It is $0$ when the player has just played the game, but not cleared. It is $1$ when the player has cleared that game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OxMuK0ZB4xQZ"
   },
   "outputs": [],
   "source": [
    "all_data.drop(columns='score_y', inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Jfn4YcfCRBtT"
   },
   "source": [
    "Presently, $0$ and $1$ labels are segregated, lets shuffle the dataframe to distribute them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aYiFbMmgZu8w"
   },
   "outputs": [],
   "source": [
    "all_data = all_data.sample(frac=1).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2hZdb4FQXzvR"
   },
   "source": [
    "### 2. Exploratory Data Analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZbHe8zKCSBzb"
   },
   "source": [
    "Let us check some data attributes before building the recommendation system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 50
    },
    "colab_type": "code",
    "id": "Nru5h8w3RypH",
    "outputId": "b35fc7e6-cb3d-494e-d48f-62d50dc53e45"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of players : 861465\n",
      "Total number of games   : 115032\n"
     ]
    }
   ],
   "source": [
    "print('Total number of players : {}'.format(len(all_data['player'].value_counts())))\n",
    "print('Total number of games   : {}'.format(len(all_data['game'].value_counts())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 50
    },
    "colab_type": "code",
    "id": "P1zV6E5fSLro",
    "outputId": "b56a7133-83cb-4f63-ac15-6da1fa4908e0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of games played and cleared     : 2051809\n",
      "Number of games played but not cleared : 2036348\n"
     ]
    }
   ],
   "source": [
    "print('Number of games played and cleared     : {}'.format(len(all_data[all_data['score_x'] == 1])))\n",
    "print('Number of games played but not cleared : {}'.format(len(all_data[all_data['score_x'] == 0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "R-rJP5acddYF"
   },
   "source": [
    "**Comment:** As we can observed from output of above cell, there is approximately $50:50$ split between game levels cleared and games only played."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NJoYH6qdSxWn"
   },
   "source": [
    "### 3. Community detection system data preparation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WxhQt4-m1uSA"
   },
   "source": [
    "Note: I have tried to generate a vector representation for each user using the 'likes' data, however, creating a high dimensional vector for each user is very slow, and it might take few days to complete it for all data. So I had to abandon that approach. An alternative approach based on the SVD recommender system seems more practical. We have a $100$ dimensional vector representation for each user generate by the SVD algorithm. This vector can be used as input to clustering algorithm. However, since we have total $861465$ users, for Girvan-Newman algorithm we will need a $861465^2$ array to hold the edge weights/connectivity data, which throws Google Colab VM out of memory. So I have developed the model for $5000$ users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XCGwuMTZ3t_-"
   },
   "outputs": [],
   "source": [
    "max_users = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gQsFpeI2EEZ6"
   },
   "outputs": [],
   "source": [
    "reader = Reader(rating_scale=(0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FR9jSUivoaOB"
   },
   "source": [
    "Since clustering is an unsupervised machine learning problem, we do not need train/val/test split. So let's generate dataset based on all data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vb5i8Pvd6mkd"
   },
   "outputs": [],
   "source": [
    "cluster_data    = Dataset.load_from_df(all_data[['player', 'game', 'score_x']], reader)\n",
    "cluster_set, _  = surprise.model_selection.train_test_split(cluster_data, test_size=1e-9) # test size cannot be zero, so using a small value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kPzKGENJFNM6"
   },
   "source": [
    "Next, we obtain vector representations for players ($100$-dimensional), by using SVD algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "C2tQnOP3FpI8"
   },
   "outputs": [],
   "source": [
    "cluster_svd = SVD(biased=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "7RO2vUjRFmTB",
    "outputId": "af73b622-2540-479d-8690-c17bc22be397"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<surprise.prediction_algorithms.matrix_factorization.SVD at 0x7f236ec81780>"
      ]
     },
     "execution_count": 23,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_svd.fit(cluster_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bOQOu8ioAYEs"
   },
   "outputs": [],
   "source": [
    "users_v = cluster_svd.pu[:max_users]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "96j9Iep5oFKv"
   },
   "source": [
    "### Baseline method: k-Means clustering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "a8_VTK43oIiN",
    "outputId": "5c942cdc-aa4e-41da-a3f1-dc37281ff2c4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of clusters: 1 \tLabels: [0 0 0 ... 0 0 0]\n",
      "Number of clusters: 3 \tLabels: [0 1 1 ... 0 0 0]\n",
      "Number of clusters: 5 \tLabels: [4 4 4 ... 1 4 3]\n",
      "Number of clusters: 7 \tLabels: [1 1 2 ... 2 4 5]\n",
      "Number of clusters: 9 \tLabels: [3 5 0 ... 2 1 0]\n",
      "Number of clusters: 11 \tLabels: [ 5  9 10 ...  3  4  1]\n",
      "Number of clusters: 13 \tLabels: [4 6 2 ... 2 7 3]\n",
      "Number of clusters: 15 \tLabels: [5 3 0 ... 2 1 4]\n",
      "Number of clusters: 17 \tLabels: [ 7  8  1 ...  7 10  2]\n",
      "Number of clusters: 19 \tLabels: [15  5 10 ... 10  8 10]\n",
      "Number of clusters: 21 \tLabels: [11  2  8 ...  1  9 10]\n",
      "Number of clusters: 23 \tLabels: [20 17  9 ... 12  5  6]\n",
      "Number of clusters: 25 \tLabels: [13  5  5 ... 13  3 18]\n",
      "Number of clusters: 27 \tLabels: [13 15  9 ...  4 24 21]\n",
      "Number of clusters: 29 \tLabels: [10 10 13 ...  2 27  5]\n",
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uZnYF8EszSwZeB+ojcTx3nwJMgVA1VCS+U6Q96dwxkctG9+PSwhwWlW7njeWb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\nItIkJQsREWmSkoWIiDRJyUJERJr0/wGys2laVOweSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "inertia = {}\n",
    "for k in range(1, 100, 2):\n",
    "    print('Number of clusters:', k, '\\tLabels:', end=' ')\n",
    "    kmeans = KMeans(n_clusters=k, max_iter=1000).fit(users_v)\n",
    "    print(kmeans.labels_)\n",
    "    inertia[k] = kmeans.inertia_ # Inertia: Sum of squared distances of samples to their closest cluster center\n",
    "plt.figure()\n",
    "plt.plot(list(inertia.keys()), list(inertia.values()))\n",
    "plt.xlabel(\"Number of cluster\")\n",
    "plt.ylabel(\"Inertia\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rd9dZnV7oL_D"
   },
   "source": [
    "### Girvan-Newman algorithm based on \"edge betweenness\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "a8q5iAjJAQpj"
   },
   "outputs": [],
   "source": [
    "sim_scores = cosine_distances(users_v,users_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "ayOKq5pBBGrr",
    "outputId": "4dfecf9e-45b0-41d3-9ab6-5e9a3eb950f6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 5000)"
      ]
     },
     "execution_count": 27,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_scores.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JevggXWq7WVo"
   },
   "outputs": [],
   "source": [
    "node1_data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "eGDTHYS7AnM1"
   },
   "outputs": [],
   "source": [
    "edge_data = pd.DataFrame(columns=['node1', 'node2', 'weight'])\n",
    "indx = 0\n",
    "for i in range(max_users):\n",
    "    print(i)\n",
    "    for j in range(i+1, max_users):\n",
    "        if sim_scores[i, j] > 0.5:\n",
    "            edge_data.loc[indx, :] = [i, j, sim_scores[i, j]]\n",
    "            indx += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "WjX7ccniFlcA"
   },
   "outputs": [],
   "source": [
    "edge_data['node1'] = edge_data['node1'].astype('int32')\n",
    "edge_data['node2'] = edge_data['node2'].astype('int32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0ZrrpwU4E2XH"
   },
   "outputs": [],
   "source": [
    "graph_file = 'edge_data.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pY9NhMmPE6Dz"
   },
   "outputs": [],
   "source": [
    "edge_data.to_csv(graph_file, sep='\\t', header=False, index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vsLLbMEYFKc7"
   },
   "outputs": [],
   "source": [
    "G = nx.Graph()\n",
    "reader = csv.reader(open(graph_file), delimiter='\\t')\n",
    "for line in reader:\n",
    "    if len(line) > 2:\n",
    "        if float(line[2]) != 0.0:\n",
    "      #line format: u,v,w\n",
    "            G.add_edge(int(line[0]),int(line[1]),weight=float(line[2]))\n",
    "        else:\n",
    "      #line format: u,v\n",
    "            G.add_edge(int(line[0]),int(line[1]),weight=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 70
    },
    "colab_type": "code",
    "id": "qwb_0KXCFPIl",
    "outputId": "7de238aa-eab5-43fb-f2cf-d07030a255af"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "G nodes: [16, 13258, 17, 357, 853, 1281, 1937, 1945, 2239, 2279, 2349, 2628, 2690, 2710, 2865, 3028, 3473, 4629, 4660, 6258, 6644, 6985, 7413, 7482, 7790, 9136, 9807, 10274, 11347, 12456, 12541, 15842, 16544, 16674, 17021, 42, 758, 1468, 3095, 3786, 4483, 5893, 5998, 6354, 6875, 7127, 7170, 11927, 16341, 17964, 20379, 21922, 23698, 65, 988, 1279, 6226, 7256, 15976, 110, 163, 891, 4301, 5755, 6048, 6215, 6496, 7856, 9400, 10224, 12591, 13825, 14851, 15122, 170, 213, 268, 3511, 7709, 12622, 285, 3653, 4944, 17167, 10206, 386, 597, 666, 9908, 11646, 11825, 13507, 879, 1153, 5543, 7207, 881, 11689, 7524, 8442, 945, 2576, 4345, 5201, 7847, 8574, 9020, 16184, 19916, 10817, 1091, 10684, 11627, 13550, 1120, 13239, 16960, 1247, 3380, 3450, 15465, 1309, 1427, 13614, 12192, 15193, 1775, 13439, 1952, 2521, 1963, 7041, 11137, 18750, 19501, 2310, 5694, 5840, 14006, 13656, 2026, 4673, 15000, 18157, 6989, 4677, 10009, 16012, 7370, 5696, 13003, 2543, 6416, 11775, 2563, 6282, 8642, 2653, 2692, 2766, 2834, 8914, 9567, 13014, 17329, 22985, 2856, 12049, 4568, 6705, 3286, 16061, 3435, 3441, 4321, 3598, 17715, 3706, 4366, 5703, 7895, 8401, 18334, 20178, 20590, 3857, 24478, 3862, 4061, 12554, 4202, 20131, 4238, 9697, 4254, 11471, 23772, 23183, 7903, 9372, 11599, 4514, 19440, 8059, 4805, 4806, 12652, 5104, 8408, 5239, 5242, 12127, 5452, 5500, 10058, 5711, 23897, 6135, 7849, 11965, 12741, 22295, 6595, 17626, 8874, 9649, 10197, 10895, 15179, 18467, 7179, 24704, 12172, 23105, 11059, 8226, 8450, 8541, 12742, 8548, 9538, 10150, 9064, 17978, 9209, 11633, 9216, 18579, 9614, 16211, 9760, 9812, 19316, 9842, 10107, 14032, 12911, 20219, 17652, 11907, 18324, 20083, 13377, 18382, 13417, 13975, 23394, 14699, 16352, 24312, 19738, 17453, 23237, 17958, 20934]\n",
      "G no of nodes: 275\n"
     ]
    }
   ],
   "source": [
    "print('G nodes:', G.nodes())\n",
    "print('G no of nodes:', G.number_of_nodes())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "K3f8xuTDGcN2"
   },
   "outputs": [],
   "source": [
    "n = G.number_of_nodes()\n",
    "A = nx.adj_matrix(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "HuDCDpnTGj1W",
    "outputId": "59209e42-ab0e-4bc4-cba5-61557db7abef"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m: 1122.0\n"
     ]
    }
   ],
   "source": [
    "m_ = 0.0    #the weighted version for number of edges\n",
    "for i in range(0,n):\n",
    "    for j in range(0,n):\n",
    "        m_ += A[i,j]\n",
    "        m_ = m_/2.0\n",
    "\n",
    "print(\"m:\", m_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "S6Lqx4ZYGmR9"
   },
   "outputs": [],
   "source": [
    "#calculate the weighted degree for each node\n",
    "Orig_deg = {}\n",
    "deg_dict = {}\n",
    "nodes = G.nodes()\n",
    "n = len(nodes)  #len(A) \n",
    "B = A.sum(axis = 1)\n",
    "i = 0\n",
    "for node_id in list(nodes):\n",
    "    deg_dict[node_id] = B[i, 0]\n",
    "    i += 1\n",
    "Orig_deg = deg_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MirGe79eNVp8"
   },
   "outputs": [],
   "source": [
    "# This method keeps removing edges from Graph until one of the connected components of Graph splits into two\n",
    "# compute the edge betweenness\n",
    "\n",
    "def CmtyGirvanNewmanStep(G):\n",
    "    print(\"Running CmtyGirvanNewmanStep method ...\")\n",
    "    init_ncomp = nx.number_connected_components(G)    #no of components\n",
    "    ncomp = init_ncomp\n",
    "    while ncomp <= init_ncomp:\n",
    "        bw = nx.edge_betweenness_centrality(G, weight='weight')    #edge betweenness for G\n",
    "        #find the edge with max centrality\n",
    "        max_ = max(bw.values())\n",
    "        #find the edge with the highest centrality and remove all of them if there is more than one!\n",
    "        for k, v in bw.items():\n",
    "            if float(v) == max_:\n",
    "                G.remove_edge(k[0],k[1])    #remove the central edge\n",
    "        ncomp = nx.number_connected_components(G)    #recalculate the no of components\n",
    "\n",
    "\n",
    "# This method compute the modularity of current split\n",
    "def _GirvanNewmanGetModularity(G, deg_, m_):\n",
    "    New_A = nx.adj_matrix(G)\n",
    "    New_deg = {}\n",
    "    New_deg = UpdateDeg(New_A, G.nodes())\n",
    "    #Let's compute the Q\n",
    "    comps = nx.connected_components(G)    #list of components    \n",
    "    print('No of communities in decomposed G:', nx.number_connected_components(G))\n",
    "    Mod = 0    #Modularity of a given partitionning\n",
    "    for c in comps:\n",
    "        EWC = 0    #no of edges within a community\n",
    "        RE = 0    #no of random edges\n",
    "        for u in c:\n",
    "            EWC += New_deg[u]\n",
    "            RE += deg_[u]        #count the probability of a random edge\n",
    "        Mod += ( float(EWC) - float(RE*RE)/float(2*m_) )\n",
    "    Mod = Mod/float(2*m_)\n",
    "    print(\"Modularity:\", Mod)\n",
    "    return Mod\n",
    "\n",
    "def UpdateDeg(A, nodes):\n",
    "    deg_dict = {}\n",
    "    n = len(nodes)  #len(A) ---> some ppl get issues when trying len() on sparse matrixes!\n",
    "    B = A.sum(axis = 1)\n",
    "    i = 0\n",
    "    for node_id in list(nodes):\n",
    "        deg_dict[node_id] = B[i, 0]\n",
    "        i += 1\n",
    "    return deg_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "gduek1AvKLFI",
    "outputId": "eeedf819-6fbd-45ae-8dcf-a4aae7fed06a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 23\n",
      "Modularity: 0.09433792152414358\n",
      "Modularity of decomposed G: 0.09433792152414358\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 17, 4629, 3095, 23105, 7709, 9760, 8226, 18467, 10274, 7207, 42, 17964, 19501, 6705, 11825, 4660, 5694, 16960, 5696, 65, 1091, 10817, 3653, 4677, 6215, 5703, 4673, 2628, 5711, 9807, 6226, 11347, 597, 7256, 2653, 15976, 13417, 15465, 20590, 110, 12911, 7790, 9842, 20083, 6258, 5239, 5242, 3706, 5755, 17021, 13439, 1153, 2690, 11907, 2692, 6282, 16012, 10895, 23183, 23698, 2710, 11927, 15000, 666, 9372, 4254, 16544, 163, 12456, 7849, 170, 8874, 7856, 9908, 14006, 9400, 11965, 16061, 2239, 13507, 4805, 4806, 3786, 13003, 7370, 4301, 2766, 11471, 5840, 8401, 20178, 6354, 8914, 213, 3286, 7895, 13014, 17626, 6875, 23772, 7903, 1247, 4321, 2279, 18157, 13550, 1775, 17652, 7413, 758, 8442, 20219, 12541, 1279, 1281, 8450, 5893, 2310, 268, 4366, 17167, 6416, 15122, 2834, 3862, 22295, 10009, 19738, 285, 1309, 16674, 2349, 13614, 12591, 2865, 17715, 11059, 3380, 7482, 18750, 6985, 10058, 15179, 5452, 6989, 12622, 11599, 4944, 853, 13656, 15193, 23897, 9567, 6496, 12127, 7524, 357, 3435, 11627, 14699, 5998, 879, 12652, 881, 3441, 3450, 891, 5500, 8059, 11646, 7041, 11137, 4483, 386, 12172, 1937, 3473, 1427, 18324, 1945, 20379, 18334, 6048, 12192, 21922, 4514, 1952, 5543, 11689, 1963, 9136, 9649, 17329, 3511, 1468, 10684, 8642, 6595, 12741, 22985, 13258, 3028, 16341, 10197, 7127, 4568, 2521, 988, 10206, 15842, 2026, 2543, 10224, 19440, 6644, 6135, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {1120, 13239}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 24\n",
      "Modularity: 0.4865233810263695\n",
      "Modularity of decomposed G: 0.4865233810263695\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 5694, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23183, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 4806, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 8914, 213, 3286, 7895, 13014, 6875, 23772, 7903, 4321, 1775, 758, 8442, 20219, 8450, 5893, 268, 4366, 6416, 15122, 2834, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 12622, 11599, 13656, 15193, 23897, 9567, 6496, 12127, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 17329, 3511, 1468, 8642, 12741, 22985, 13258, 16341, 10197, 7127, 2543, 10224, 19440, 11775}, {17, 4629, 9760, 10274, 19501, 11825, 4660, 5696, 65, 10817, 1091, 2628, 3653, 4673, 4677, 23105, 9807, 6226, 11347, 597, 7256, 15976, 15465, 7790, 6258, 20083, 17021, 2690, 11907, 2692, 16012, 2710, 15000, 16544, 12456, 7849, 8874, 14006, 16061, 2239, 13507, 7370, 13003, 5840, 17626, 1247, 2279, 18157, 13550, 17652, 7413, 12541, 1279, 1281, 2310, 17167, 285, 1309, 16674, 2349, 13614, 2865, 17715, 3380, 7482, 18750, 6985, 6989, 4944, 853, 357, 14699, 11627, 12652, 3441, 3450, 8059, 11646, 7041, 386, 11137, 1937, 3473, 1427, 1945, 18334, 1952, 1963, 9136, 10684, 6595, 3028, 4568, 2521, 988, 10206, 15842, 2026, 6644, 6135}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {1120, 13239}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 25\n",
      "Modularity: 0.4903672617969567\n",
      "Modularity of decomposed G: 0.4903672617969567\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 5694, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23183, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 4806, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 8914, 213, 13014, 7895, 6875, 23772, 7903, 4321, 1775, 758, 8442, 20219, 5893, 4366, 15122, 2834, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 9567, 6496, 12127, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 17329, 1468, 8642, 12741, 22985, 13258, 16341, 10197, 7127, 10224, 19440}, {17, 4629, 9760, 10274, 19501, 11825, 4660, 5696, 65, 10817, 1091, 2628, 3653, 4673, 4677, 23105, 9807, 6226, 11347, 597, 7256, 15976, 15465, 7790, 6258, 20083, 17021, 2690, 11907, 2692, 16012, 2710, 15000, 16544, 12456, 7849, 8874, 14006, 16061, 2239, 13507, 7370, 13003, 5840, 17626, 1247, 2279, 18157, 13550, 17652, 7413, 12541, 1279, 1281, 2310, 17167, 285, 1309, 16674, 2349, 13614, 2865, 17715, 3380, 7482, 18750, 6985, 6989, 4944, 853, 357, 14699, 11627, 12652, 3441, 3450, 8059, 11646, 7041, 386, 11137, 1937, 3473, 1427, 1945, 18334, 1952, 1963, 9136, 10684, 6595, 3028, 4568, 2521, 988, 10206, 15842, 2026, 6644, 6135}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {1120, 13239}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 26\n",
      "Modularity: 0.49897488569240694\n",
      "Modularity of decomposed G: 0.49897488569240694\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 5694, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23183, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 4806, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 8914, 213, 13014, 7895, 6875, 23772, 7903, 4321, 1775, 758, 8442, 20219, 5893, 4366, 15122, 2834, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 9567, 6496, 12127, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 17329, 1468, 8642, 12741, 22985, 13258, 16341, 10197, 7127, 10224, 19440}, {17, 4629, 10274, 19501, 11825, 4660, 5696, 65, 10817, 1091, 2628, 3653, 4673, 4677, 23105, 9807, 6226, 11347, 597, 7256, 15976, 15465, 7790, 6258, 20083, 17021, 2690, 2692, 2710, 15000, 16544, 12456, 7849, 8874, 14006, 16061, 2239, 13507, 7370, 13003, 5840, 17626, 1247, 2279, 18157, 13550, 7413, 12541, 1279, 1281, 17167, 285, 1309, 16674, 2349, 13614, 2865, 17715, 3380, 7482, 18750, 6985, 6989, 4944, 853, 357, 14699, 12652, 3441, 3450, 8059, 11646, 7041, 386, 11137, 1937, 3473, 1427, 1945, 18334, 1952, 1963, 9136, 10684, 6595, 3028, 4568, 2521, 988, 10206, 15842, 2026, 6644, 6135}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 27\n",
      "Modularity: 0.5047939285907199\n",
      "Modularity of decomposed G: 0.5047939285907199\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 5694, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23183, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 4806, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 8914, 213, 13014, 7895, 6875, 23772, 7903, 4321, 1775, 758, 8442, 20219, 5893, 4366, 15122, 2834, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 9567, 6496, 12127, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 17329, 1468, 8642, 12741, 22985, 13258, 16341, 10197, 7127, 10224, 19440}, {17, 4629, 10274, 19501, 11825, 4660, 23105, 65, 10817, 2628, 3653, 1091, 4673, 9807, 6226, 11347, 597, 7256, 15976, 15465, 7790, 6258, 17021, 2690, 2692, 2710, 15000, 16544, 12456, 7849, 8874, 14006, 16061, 2239, 13507, 7370, 5840, 17626, 1247, 2279, 18157, 13550, 7413, 12541, 1279, 1281, 17167, 285, 1309, 16674, 2349, 13614, 2865, 3380, 7482, 18750, 6985, 6989, 4944, 853, 357, 14699, 12652, 3441, 3450, 11646, 7041, 386, 11137, 1937, 3473, 1427, 1945, 1952, 1963, 9136, 10684, 6595, 3028, 4568, 988, 10206, 15842, 6644, 6135}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {5696, 4677, 2026, 13003, 20083, 17715, 2521, 8059, 18334}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 28\n",
      "Modularity: 0.504524245283918\n",
      "Modularity of decomposed G: 0.504524245283918\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 29\n",
      "Modularity: 0.5079931907943862\n",
      "Modularity of decomposed G: 0.5079931907943862\n",
      "Components: [{13825, 7170, 14851, 2563, 3598, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 5694, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23183, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 213, 13014, 7895, 6875, 23772, 7903, 4321, 1775, 758, 8442, 20219, 5893, 4366, 15122, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 12127, 6496, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 1468, 8642, 12741, 13258, 16341, 10197, 7127, 10224, 19440}, {1281, 2690, 386, 2692, 11137, 17167, 17, 1937, 3473, 1427, 4629, 2710, 15000, 1945, 285, 1309, 16544, 1952, 10274, 16674, 12456, 1963, 2349, 13614, 19501, 9136, 2865, 11825, 4660, 3380, 14006, 7482, 10684, 16061, 18750, 2239, 65, 10817, 13507, 2628, 3653, 1091, 4673, 6595, 6985, 7370, 6989, 9807, 4944, 5840, 6226, 11347, 3028, 853, 597, 7256, 4568, 17626, 988, 10206, 1247, 15842, 357, 2279, 15976, 15465, 14699, 12652, 18157, 7790, 13550, 3441, 6258, 6644, 7413, 12541, 3450, 17021, 11646, 1279}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {5696, 4677, 2026, 13003, 20083, 17715, 2521, 8059, 18334}, {23105, 7041, 7849, 8874, 6135}, {4806, 22985, 17329, 2834, 8914, 9567}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 30\n",
      "Modularity: 0.5099901976671402\n",
      "Modularity of decomposed G: 0.5099901976671402\n",
      "Components: [{13825, 7170, 14851, 2563, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 213, 13014, 7895, 6875, 23772, 7903, 1775, 758, 8442, 20219, 5893, 4366, 15122, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 12127, 6496, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 1468, 8642, 12741, 13258, 16341, 10197, 7127, 10224, 19440}, {1281, 2690, 386, 2692, 11137, 17167, 17, 1937, 3473, 1427, 4629, 2710, 15000, 1945, 285, 1309, 16544, 1952, 10274, 16674, 12456, 1963, 2349, 13614, 19501, 9136, 2865, 11825, 4660, 3380, 14006, 7482, 10684, 16061, 18750, 2239, 65, 10817, 13507, 2628, 3653, 1091, 4673, 6595, 6985, 7370, 6989, 9807, 4944, 5840, 6226, 11347, 3028, 853, 597, 7256, 4568, 17626, 988, 10206, 1247, 15842, 357, 2279, 15976, 15465, 14699, 12652, 18157, 7790, 13550, 3441, 6258, 6644, 7413, 12541, 3450, 17021, 11646, 1279}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {5696, 4677, 2026, 13003, 20083, 17715, 2521, 8059, 18334}, {23105, 7041, 7849, 8874, 6135}, {23183, 4321, 5694, 3598}, {4806, 22985, 17329, 2834, 8914, 9567}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 31\n",
      "Modularity: 0.5079288480908488\n",
      "Modularity of decomposed G: 0.5079288480908488\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 32\n",
      "Modularity: 0.5027726939098439\n",
      "Modularity of decomposed G: 0.5027726939098439\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 33\n",
      "Modularity: 0.50121893677257\n",
      "Modularity of decomposed G: 0.50121893677257\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 34\n",
      "Modularity: 0.5006049008486884\n",
      "Modularity of decomposed G: 0.5006049008486884\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 35\n",
      "Modularity: 0.5002760381417193\n",
      "Modularity of decomposed G: 0.5002760381417193\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 36\n",
      "Modularity: 0.4989391397459973\n",
      "Modularity of decomposed G: 0.4989391397459973\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 37\n",
      "Modularity: 0.4955027627644804\n",
      "Modularity of decomposed G: 0.4955027627644804\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 38\n",
      "Modularity: 0.49409397529875676\n",
      "Modularity of decomposed G: 0.49409397529875676\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 71\n",
      "Modularity: 0.4756252363204235\n",
      "Modularity of decomposed G: 0.4756252363204235\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 72\n",
      "Modularity: 0.47582541362031755\n",
      "Modularity of decomposed G: 0.47582541362031755\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 73\n",
      "Modularity: 0.4806435700191598\n",
      "Modularity of decomposed G: 0.4806435700191598\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 74\n",
      "Modularity: 0.47983571163030114\n",
      "Modularity of decomposed G: 0.47983571163030114\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 75\n",
      "Modularity: 0.47853853095281224\n",
      "Modularity of decomposed G: 0.47853853095281224\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 76\n",
      "Modularity: 0.4772397615665939\n",
      "Modularity of decomposed G: 0.4772397615665939\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 77\n",
      "Modularity: 0.4764303144690059\n",
      "Modularity of decomposed G: 0.4764303144690059\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 78\n",
      "Modularity: 0.47280408679433533\n",
      "Modularity of decomposed G: 0.47280408679433533\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 79\n",
      "Modularity: 0.4711565958420315\n",
      "Modularity of decomposed G: 0.4711565958420315\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 80\n",
      "Modularity: 0.4699388506010085\n",
      "Modularity of decomposed G: 0.4699388506010085\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 81\n",
      "Modularity: 0.4696818769640412\n",
      "Modularity of decomposed G: 0.4696818769640412\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 82\n",
      "Modularity: 0.4688644863228066\n",
      "Modularity of decomposed G: 0.4688644863228066\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 83\n",
      "Modularity: 0.4685260913634617\n",
      "Modularity of decomposed G: 0.4685260913634617\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 84\n",
      "Modularity: 0.4663098426860617\n",
      "Modularity of decomposed G: 0.4663098426860617\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 85\n",
      "Modularity: 0.4660330101899778\n",
      "Modularity of decomposed G: 0.4660330101899778\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 86\n",
      "Modularity: 0.4649332265721068\n",
      "Modularity of decomposed G: 0.4649332265721068\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 87\n",
      "Modularity: 0.46070805570648293\n",
      "Modularity of decomposed G: 0.46070805570648293\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 88\n",
      "Modularity: 0.4560038891589694\n",
      "Modularity of decomposed G: 0.4560038891589694\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 89\n",
      "Modularity: 0.4565325319886503\n",
      "Modularity of decomposed G: 0.4565325319886503\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 90\n",
      "Modularity: 0.4553767463880708\n",
      "Modularity of decomposed G: 0.4553767463880708\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 91\n",
      "Modularity: 0.454137553579202\n",
      "Modularity of decomposed G: 0.454137553579202\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 92\n",
      "Modularity: 0.45808072864537175\n",
      "Modularity of decomposed G: 0.45808072864537175\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 93\n",
      "Modularity: 0.45603010285300327\n",
      "Modularity of decomposed G: 0.45603010285300327\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 95\n",
      "Modularity: 0.4543961159248987\n",
      "Modularity of decomposed G: 0.4543961159248987\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 96\n",
      "Modularity: 0.45313666707973105\n",
      "Modularity of decomposed G: 0.45313666707973105\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 97\n",
      "Modularity: 0.452586179505022\n",
      "Modularity of decomposed G: 0.452586179505022\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 98\n",
      "Modularity: 0.45090055954321456\n",
      "Modularity of decomposed G: 0.45090055954321456\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 99\n",
      "Modularity: 0.44878360516139704\n",
      "Modularity of decomposed G: 0.44878360516139704\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 100\n",
      "Modularity: 0.4455450224166803\n",
      "Modularity of decomposed G: 0.4455450224166803\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 101\n",
      "Modularity: 0.44430940420245246\n",
      "Modularity of decomposed G: 0.44430940420245246\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 102\n",
      "Modularity: 0.44299871950076436\n",
      "Modularity of decomposed G: 0.44299871950076436\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 103\n",
      "Modularity: 0.4413234261456975\n",
      "Modularity of decomposed G: 0.4413234261456975\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 104\n",
      "Modularity: 0.43942968534034926\n",
      "Modularity of decomposed G: 0.43942968534034926\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 105\n",
      "Modularity: 0.43730717047797907\n",
      "Modularity of decomposed G: 0.43730717047797907\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 106\n",
      "Modularity: 0.43514454072019354\n",
      "Modularity of decomposed G: 0.43514454072019354\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 107\n",
      "Modularity: 0.4330522113236805\n",
      "Modularity of decomposed G: 0.4330522113236805\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 108\n",
      "Modularity: 0.429229778120939\n",
      "Modularity of decomposed G: 0.429229778120939\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 109\n",
      "Modularity: 0.42751158963018054\n",
      "Modularity of decomposed G: 0.42751158963018054\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 110\n",
      "Modularity: 0.42470275259674456\n",
      "Modularity of decomposed G: 0.42470275259674456\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 111\n",
      "Modularity: 0.4225301934094009\n",
      "Modularity of decomposed G: 0.4225301934094009\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 112\n",
      "Modularity: 0.420419991039683\n",
      "Modularity of decomposed G: 0.420419991039683\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 113\n",
      "Modularity: 0.41867082272870276\n",
      "Modularity of decomposed G: 0.41867082272870276\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 114\n",
      "Modularity: 0.4156919938612296\n",
      "Modularity of decomposed G: 0.4156919938612296\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 115\n",
      "Modularity: 0.4099166404529728\n",
      "Modularity of decomposed G: 0.4099166404529728\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 116\n",
      "Modularity: 0.4090587377391406\n",
      "Modularity of decomposed G: 0.4090587377391406\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 117\n",
      "Modularity: 0.40623242490968214\n",
      "Modularity of decomposed G: 0.40623242490968214\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 118\n",
      "Modularity: 0.4026562415599851\n",
      "Modularity of decomposed G: 0.4026562415599851\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 119\n",
      "Modularity: 0.40041377918855137\n",
      "Modularity of decomposed G: 0.40041377918855137\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 120\n",
      "Modularity: 0.3995630256640011\n",
      "Modularity of decomposed G: 0.3995630256640011\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 121\n",
      "Modularity: 0.3968737389624463\n",
      "Modularity of decomposed G: 0.3968737389624463\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 122\n",
      "Modularity: 0.3932705475643509\n",
      "Modularity of decomposed G: 0.3932705475643509\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 123\n",
      "Modularity: 0.3915841332481788\n",
      "Modularity of decomposed G: 0.3915841332481788\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 124\n",
      "Modularity: 0.39097764369076127\n",
      "Modularity of decomposed G: 0.39097764369076127\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 125\n",
      "Modularity: 0.38713495445172097\n",
      "Modularity of decomposed G: 0.38713495445172097\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 126\n",
      "Modularity: 0.38634218879579085\n",
      "Modularity of decomposed G: 0.38634218879579085\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 139\n",
      "Modularity: 0.374114294883405\n",
      "Modularity of decomposed G: 0.374114294883405\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 140\n",
      "Modularity: 0.3693815315787637\n",
      "Modularity of decomposed G: 0.3693815315787637\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 141\n",
      "Modularity: 0.3650693789102097\n",
      "Modularity of decomposed G: 0.3650693789102097\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 142\n",
      "Modularity: 0.36249169899688966\n",
      "Modularity of decomposed G: 0.36249169899688966\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 143\n",
      "Modularity: 0.3607655669624846\n",
      "Modularity of decomposed G: 0.3607655669624846\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 144\n",
      "Modularity: 0.3564367328522727\n",
      "Modularity of decomposed G: 0.3564367328522727\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 145\n",
      "Modularity: 0.3535889724549684\n",
      "Modularity of decomposed G: 0.3535889724549684\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 146\n",
      "Modularity: 0.34898251149430803\n",
      "Modularity of decomposed G: 0.34898251149430803\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 147\n",
      "Modularity: 0.34446938717149517\n",
      "Modularity of decomposed G: 0.34446938717149517\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 148\n",
      "Modularity: 0.3397977891529326\n",
      "Modularity of decomposed G: 0.3397977891529326\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 151\n",
      "Modularity: 0.33717165362336843\n",
      "Modularity of decomposed G: 0.33717165362336843\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 152\n",
      "Modularity: 0.33221329367916386\n",
      "Modularity of decomposed G: 0.33221329367916386\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 153\n",
      "Modularity: 0.32658330711963973\n",
      "Modularity of decomposed G: 0.32658330711963973\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 154\n",
      "Modularity: 0.32249079343291404\n",
      "Modularity of decomposed G: 0.32249079343291404\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 155\n",
      "Modularity: 0.31730524814041683\n",
      "Modularity of decomposed G: 0.31730524814041683\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 156\n",
      "Modularity: 0.312811585499538\n",
      "Modularity of decomposed G: 0.312811585499538\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 157\n",
      "Modularity: 0.30926797067879197\n",
      "Modularity of decomposed G: 0.30926797067879197\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 158\n",
      "Modularity: 0.3083830599165613\n",
      "Modularity of decomposed G: 0.3083830599165613\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 159\n",
      "Modularity: 0.303316667778763\n",
      "Modularity of decomposed G: 0.303316667778763\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 160\n",
      "Modularity: 0.29753773977586523\n",
      "Modularity of decomposed G: 0.29753773977586523\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 161\n",
      "Modularity: 0.29197169874269613\n",
      "Modularity of decomposed G: 0.29197169874269613\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 162\n",
      "Modularity: 0.28622375056002003\n",
      "Modularity of decomposed G: 0.28622375056002003\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 163\n",
      "Modularity: 0.2806394393764638\n",
      "Modularity of decomposed G: 0.2806394393764638\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 175\n",
      "Modularity: 0.270029248127707\n",
      "Modularity of decomposed G: 0.270029248127707\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 176\n",
      "Modularity: 0.2628228653315161\n",
      "Modularity of decomposed G: 0.2628228653315161\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 177\n",
      "Modularity: 0.2575499410589064\n",
      "Modularity of decomposed G: 0.2575499410589064\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 178\n",
      "Modularity: 0.2492934217926356\n",
      "Modularity of decomposed G: 0.2492934217926356\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 179\n",
      "Modularity: 0.24382071739731406\n",
      "Modularity of decomposed G: 0.24382071739731406\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 180\n",
      "Modularity: 0.23558167392706575\n",
      "Modularity of decomposed G: 0.23558167392706575\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 181\n",
      "Modularity: 0.2272778905760978\n",
      "Modularity of decomposed G: 0.2272778905760978\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 182\n",
      "Modularity: 0.2181785613289233\n",
      "Modularity of decomposed G: 0.2181785613289233\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 183\n",
      "Modularity: 0.21162990394667044\n",
      "Modularity of decomposed G: 0.21162990394667044\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 184\n",
      "Modularity: 0.2068494793801496\n",
      "Modularity of decomposed G: 0.2068494793801496\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 185\n",
      "Modularity: 0.19988100571617423\n",
      "Modularity of decomposed G: 0.19988100571617423\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 186\n",
      "Modularity: 0.19215749822859\n",
      "Modularity of decomposed G: 0.19215749822859\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 187\n",
      "Modularity: 0.1914235147956446\n",
      "Modularity of decomposed G: 0.1914235147956446\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 188\n",
      "Modularity: 0.18625385659044064\n",
      "Modularity of decomposed G: 0.18625385659044064\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 189\n",
      "Modularity: 0.17728082968724704\n",
      "Modularity of decomposed G: 0.17728082968724704\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 190\n",
      "Modularity: 0.16396705335837158\n",
      "Modularity of decomposed G: 0.16396705335837158\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 191\n",
      "Modularity: 0.16073085367674883\n",
      "Modularity of decomposed G: 0.16073085367674883\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 192\n",
      "Modularity: 0.15370399496697093\n",
      "Modularity of decomposed G: 0.15370399496697093\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 194\n",
      "Modularity: 0.13185686687574075\n",
      "Modularity of decomposed G: 0.13185686687574075\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 195\n",
      "Modularity: 0.12383547650140926\n",
      "Modularity of decomposed G: 0.12383547650140926\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 196\n",
      "Modularity: 0.12667330746915528\n",
      "Modularity of decomposed G: 0.12667330746915528\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 197\n",
      "Modularity: 0.11908563457792784\n",
      "Modularity of decomposed G: 0.11908563457792784\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 198\n",
      "Modularity: 0.11822137702917832\n",
      "Modularity of decomposed G: 0.11822137702917832\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 200\n",
      "Modularity: 0.10797658878816485\n",
      "Modularity of decomposed G: 0.10797658878816485\n",
      "Running CmtyGirvanNewmanStep method ...\n",
      "No of communities in decomposed G: 275\n",
      "Modularity: -0.009612084989562142\n",
      "Modularity of decomposed G: -0.009612084989562142\n",
      "Max modularity (Q): 0.5099901976671402\n",
      "Graph communities: [{13825, 7170, 14851, 2563, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 213, 13014, 7895, 6875, 23772, 7903, 1775, 758, 8442, 20219, 5893, 4366, 15122, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 12127, 6496, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 1468, 8642, 12741, 13258, 16341, 10197, 7127, 10224, 19440}, {1281, 2690, 386, 2692, 11137, 17167, 17, 1937, 3473, 1427, 4629, 2710, 15000, 1945, 285, 1309, 16544, 1952, 10274, 16674, 12456, 1963, 2349, 13614, 19501, 9136, 2865, 11825, 4660, 3380, 14006, 7482, 10684, 16061, 18750, 2239, 65, 10817, 13507, 2628, 3653, 1091, 4673, 6595, 6985, 7370, 6989, 9807, 4944, 5840, 6226, 11347, 3028, 853, 597, 7256, 4568, 17626, 988, 10206, 1247, 15842, 357, 2279, 15976, 15465, 14699, 12652, 18157, 7790, 13550, 3441, 6258, 6644, 7413, 12541, 3450, 17021, 11646, 1279}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {5696, 4677, 2026, 13003, 20083, 17715, 2521, 8059, 18334}, {23105, 7041, 7849, 8874, 6135}, {23183, 4321, 5694, 3598}, {4806, 22985, 17329, 2834, 8914, 9567}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n"
     ]
    }
   ],
   "source": [
    "#let's find the best split of the graph\n",
    "BestQ = 0.0\n",
    "Q = 0.0\n",
    "while True:    \n",
    "    CmtyGirvanNewmanStep(G)\n",
    "    Q = _GirvanNewmanGetModularity(G, Orig_deg, m_);\n",
    "    print(\"Modularity of decomposed G:\", Q)\n",
    "    if Q > BestQ:\n",
    "        BestQ = Q\n",
    "        Bestcomps = list(nx.connected_components(G))    #Best Split\n",
    "        print(\"Components:\", Bestcomps)\n",
    "    if G.number_of_edges() == 0:\n",
    "        break\n",
    "if BestQ > 0.0:\n",
    "    print(\"Max modularity (Q):\", BestQ)\n",
    "    print(\"Graph communities:\", Bestcomps)\n",
    "else:\n",
    "    print(\"Max modularity (Q):\", BestQ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 87
    },
    "colab_type": "code",
    "id": "X4FyRQu1Gxm9",
    "outputId": "87caef59-46d1-47b7-d0fe-5d43a57d2d1c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max modularity (Q): 0.5099901976671402\n",
      "Number of communities: 30\n",
      "Graph communities: [{13825, 7170, 14851, 2563, 16, 3095, 7709, 8226, 18467, 7207, 42, 17964, 6705, 16960, 6215, 5703, 5711, 2653, 13417, 20590, 110, 12911, 9842, 5239, 5242, 3706, 5755, 13439, 1153, 6282, 10895, 23698, 11927, 666, 9372, 4254, 163, 170, 7856, 9908, 9400, 11965, 4805, 3786, 4301, 2766, 11471, 8401, 20178, 6354, 213, 13014, 7895, 6875, 23772, 7903, 1775, 758, 8442, 20219, 5893, 4366, 15122, 3862, 22295, 10009, 19738, 12591, 11059, 10058, 15179, 5452, 11599, 15193, 23897, 12127, 6496, 7524, 3435, 5998, 879, 881, 891, 5500, 4483, 12172, 18324, 20379, 6048, 12192, 21922, 4514, 5543, 11689, 9649, 1468, 8642, 12741, 13258, 16341, 10197, 7127, 10224, 19440}, {1281, 2690, 386, 2692, 11137, 17167, 17, 1937, 3473, 1427, 4629, 2710, 15000, 1945, 285, 1309, 16544, 1952, 10274, 16674, 12456, 1963, 2349, 13614, 19501, 9136, 2865, 11825, 4660, 3380, 14006, 7482, 10684, 16061, 18750, 2239, 65, 10817, 13507, 2628, 3653, 1091, 4673, 6595, 6985, 7370, 6989, 9807, 4944, 5840, 6226, 11347, 3028, 853, 597, 7256, 4568, 17626, 988, 10206, 1247, 15842, 357, 2279, 15976, 15465, 14699, 12652, 18157, 7790, 13550, 3441, 6258, 6644, 7413, 12541, 3450, 17021, 11646, 1279}, {8450, 268, 12622, 2543, 6416, 3286, 3511, 13656, 11775}, {10150, 7847, 19916, 2576, 945, 5201, 16184, 4345, 9020, 8574}, {9760, 11907, 2310, 11627, 16012, 17652}, {1120, 13239}, {5696, 4677, 2026, 13003, 20083, 17715, 2521, 8059, 18334}, {23105, 7041, 7849, 8874, 6135}, {23183, 4321, 5694, 3598}, {4806, 22985, 17329, 2834, 8914, 9567}, {2856, 12049}, {3857, 24478}, {12554, 4061}, {4202, 20131}, {9697, 4238}, {5104, 8408}, {24704, 7179}, {8541, 12742}, {9538, 8548}, {9064, 17978}, {9209, 11633}, {9216, 18579}, {16211, 9614}, {19316, 9812}, {14032, 10107}, {13377, 18382}, {23394, 13975}, {16352, 24312}, {23237, 17453}, {20934, 17958}]\n"
     ]
    }
   ],
   "source": [
    "print(\"Max modularity (Q):\", BestQ)\n",
    "print(\"Number of communities:\", len(Bestcomps))\n",
    "print(\"Graph communities:\", Bestcomps)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "S5wrCOaNHgbI"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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   "collapsed_sections": [],
   "name": "SMM_Community.ipynb",
   "provenance": []
  },
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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