04_network_centrality_01.ipynb

04_network_centrality_02.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Path lengths distribution, and Average degree of separation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import networkx as nx \n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "import pandas as pd\n",
    "plt.rcParams['figure.figsize']=[15,7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#g = nx.gnp_random_graph(500,0.1)\n",
    "g = nx.read_edgelist(\"data/facebook.txt\",delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113af70b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Path lengths distribution (way 1)\n",
    "path_lengths1 = []\n",
    "for n1 in g.nodes():\n",
    "    for n2 in g.nodes():\n",
    "        if n1 != n2 and nx.has_path(g,n1,n2):\n",
    "            path_lengths1.append(nx.shortest_path_length(g,n1,n2)) #Returns the shortest path length between two nodes n1,n2 (integer value to represent the length)\n",
    "\n",
    "#Another way (way 2)\n",
    "path_lengths2 = []\n",
    "for n1 in g.nodes():\n",
    "    for n2 in g.nodes():\n",
    "        if n1 != n2 and nx.has_path(g,n1,n2):\n",
    "            path_lengths2.append(len(nx.shortest_path(g,n1,n2))-1) #Returns the shortest path between two nodes n1,n2 (list to represent the length)\n",
    "\n",
    "#Another way (way 3)\n",
    "path_lengths3 = []\n",
    "for n in g.nodes():\n",
    "    paths = nx.single_source_shortest_path(g,n) # Returns the shortest paths between the node n and all the other nodes in the graph (dictionary key = target_node, value = list of nodes to represent a path) \n",
    "    for path in paths.values():\n",
    "        if len(path)!=1:\n",
    "            path_lengths3.append (len(path)-1)\n",
    "\n",
    "#Another way (way 4)\n",
    "path_lengths4 = []\n",
    "for n in g.nodes():\n",
    "    lengths=nx.single_source_shortest_path_length(g,n) #Returns the shortest paths between the node n and all the other nodes in the graph (dictionary key = target_node, value = integer value to represent a path length)\n",
    "    for length in lengths.values():\n",
    "        if length !=0:\n",
    "            path_lengths4.append(length)\n",
    "\n",
    "            \n",
    "figs,axes = plt.subplots(1,4)\n",
    "axes[0].hist(path_lengths1)\n",
    "axes[0].set_title(\"Way 1\")\n",
    "\n",
    "axes[1].hist(path_lengths2)\n",
    "axes[1].set_title(\"Way 2\")\n",
    "\n",
    "axes[2].hist(path_lengths3)\n",
    "axes[2].set_title(\"Way 3\")\n",
    "\n",
    "axes[3].hist(path_lengths3)\n",
    "axes[3].set_title(\"Way 4\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gyr+fA+h5AiIFWS8WW8bMrjCzKYQrhmcVeYmISDuT9UhgCKEr6DXABODLagUk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\nzP97fYewwdoT+GeifI8icRw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1171ebfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Average Path Length Distribution\n",
    "avg_path_lengths = []\n",
    "for n in g.nodes():\n",
    "    shortest_paths_lengths= nx.single_source_shortest_path_length(g,n).values()\n",
    "    avg_path_lengths.append(sum(shortest_paths_lengths)/len(shortest_paths_lengths))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.hist(avg_path_lengths,bins=12)\n",
    "ax.axvline(nx.average_shortest_path_length(g), color='red',linestyle ='dashed')\n",
    "ax.set_xlabel('Average path length', fontsize=15)\n",
    "ax.set_ylabel('Number of nodes', fontsize=15)\n",
    "ax.set_title('Average degrees of separation', fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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04_network_centrality_03.ipynb