Girvan–Newman algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PtTiIiopi3rx5bN682TM2tCgCLOfP5/r5e9hO8voR29GQDr9y5uPIQzGOvn5K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\n+YY5nxqeE48AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xfb82ee76a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "G=nx.Graph()\n",
    "G.add_edge(1,2)\n",
    "G.add_edge(1,3)\n",
    "G.add_edge(1,4)\n",
    "G.add_edge(2,3)\n",
    "G.add_edge(3,4)\n",
    "G.add_edge(4,5)\n",
    "G.add_edge(4,6)\n",
    "G.add_edge(5,6)\n",
    "G.add_edge(5,7)\n",
    "G.add_edge(6,7)\n",
    "G.add_edge(5,8)\n",
    "G.add_edge(6,8)\n",
    "G.add_edge(7,8)\n",
    "G.add_edge(7,9)\n",
    "\n",
    "\n",
    "nx.draw(G, with_labels=True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find edge with highest betweeness centrality\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2): 4.0, (1, 3): 1.0, (1, 4): 9.0, (2, 3): 4.0, (3, 4): 9.0, (4, 5): 10.0, (4, 6): 10.0, (5, 6): 1.0, (5, 7): 6.0, (5, 8): 3.0, (6, 7): 6.0, (6, 8): 3.0, (7, 8): 2.0, (7, 9): 8.0}\n",
      "10.0\n",
      "(4, 5)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "eb=nx.edge_betweenness_centrality(G, normalized=False)\n",
    "print(eb)\n",
    "\n",
    "\n",
    "def get_max_betweeness_edge():\n",
    "    max = 0\n",
    "    max_edge = ()\n",
    "    for k, v in eb.items():\n",
    "        if v > max:\n",
    "            max = v \n",
    "            max_edge=k\n",
    "    return max, max_edge\n",
    "\n",
    "(max,max_edge) = get_max_betweeness_edge()\n",
    "\n",
    "print(max)\n",
    "print(max_edge)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Remove edge with highest between centrality\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R0dEkJSUxefJk+/63DXDlyhW2bt3qCN3c3FyGDx/u6F6OjIzE19fXZbV7q+nTp9O/f3+m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\nmEQhLCIiYhKFsIiIiEkUwiIiIib5f72mpHIbHxudAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xfb8384fb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.remove_edge(max_edge[0],max_edge[1])\n",
    "nx.draw(G, with_labels=True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find edge with highest betweeness centrality in the new graph and delete the edge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2): 4.0, (1, 3): 1.0, (1, 4): 9.0, (2, 3): 4.0, (3, 4): 9.0, (4, 6): 20.0, (5, 6): 5.0, (5, 7): 2.0, (5, 8): 1.0, (6, 7): 10.0, (6, 8): 5.0, (7, 8): 2.0, (7, 9): 8.0}\n",
      "20.0\n",
      "(4, 6)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xfb83f84b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eb=nx.edge_betweenness_centrality(G, normalized=False)\n",
    "print(eb)\n",
    "\n",
    "(max,max_edge) = get_max_betweeness_edge()\n",
    "print(max)\n",
    "print(max_edge)\n",
    "G.remove_edge(max_edge[0],max_edge[1])\n",
    "nx.draw(G, with_labels=True)\n",
    "plt.show()\n",
    "      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find edge with highest betweeness centrality in the new graph and delete the edge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2): 1.5, (1, 3): 1.0, (1, 4): 1.5, (2, 3): 1.5, (3, 4): 1.5, (5, 6): 1.0, (5, 7): 2.0, (5, 8): 1.0, (6, 7): 2.0, (6, 8): 1.0, (7, 8): 2.0, (7, 9): 4.0}\n",
      "4.0\n",
      "(7, 9)\n"
     ]
    },
    {
     "data": {
      "image/png": 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Waeo7byWqZPVCtvcp8/rOw8mRsCSNVmnqO28EdgNvB84FmoG1wMWp7jEK6jsP\nJ1dHS9JolWZ19GGiZ8JJzUSh3AIMWL88Cuo7DydHwpI0WtXWRrWgY7E+h6uIRsDJr4lAJSkCOBaL\n9vYawHlzJCxJo9kQKmaNlvrOw8mRsCSNZvX1UZnIqqrcrhtF9Z2Hk6ujJWm0S9Zptr7ziHM6WpIU\nsb7ziDOEJUl9Wd95xBjCkiQF4sIsSZICMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBD\nWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrE\nEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKkQAxhSZIC\nMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKkQAxhSZICMYQlSQrEEJYkKRBDWJKk\nQAxhSZICMYQlSQrk/wOg0JRurJIOBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xfb83bc6ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eb=nx.edge_betweenness_centrality(G, normalized=False)\n",
    "print(eb)\n",
    "\n",
    "(max,max_edge) = get_max_betweeness_edge()\n",
    "print(max)\n",
    "print(max_edge)\n",
    "G.remove_edge(max_edge[0],max_edge[1])\n",
    "nx.draw(G, with_labels=True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}