hybrid_graphs.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from itertools import chain\n",
      "import networkx as nx\n",
      "import matplotlib.pyplot as plt\n",
      "from networkx.generators.random_graphs import _random_subset"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.rcParams['figure.figsize'] = (12, 7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Hybrid graph generator - tunable random/preferential attachment. Based on Mathew Jackson's Coursera course Social and Economic Networks https://www.coursera.org/course/networksonline"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simple_hybrid_graph(t, m=2, alpha=0.5):\n",
      "    \"\"\"Generates a random graph that uses a mixed model for growth. \n",
      "       For each unit of time t, a new node links to the graph with \n",
      "       m * alpha links assigned randomly to existing nodes, and \n",
      "       m * (1 - alpha) links assigned to neighbors of the above random nodes.\n",
      "       alpha near 1 produces a nearly exponential degree distribution, \n",
      "       alpha near 0 produces a nearly preferential (scale free) \n",
      "       degree distribution.\n",
      "       IMPORTANT: m % alpha == 0\"\"\"\n",
      "    beta = 1 - alpha\n",
      "    random = int(alpha * m)\n",
      "    preferential = int(beta * m)\n",
      "    G = nx.empty_graph(random)\n",
      "    targets = list(range(random))\n",
      "    source = random\n",
      "    while source < t:\n",
      "        G.add_edges_from(zip([source] * random, targets))\n",
      "        neighbors = chain.from_iterable([G.neighbors(node) \n",
      "                                         for node in targets])\n",
      "        neighbors = filter(lambda x: x != source, neighbors)\n",
      "        # Grows randomly with alpha * m # of links until there is a\n",
      "        # neighbor, then adds all neighbors until len of neighbors is\n",
      "        # greater than # of preferential neighbors to be added. After\n",
      "        # random selection, preferential attachment of neighbors begins \n",
      "        # normally.\n",
      "        if len(neighbors) > preferential:\n",
      "            neighbor_targets = _random_subset(neighbors, preferential)\n",
      "            G.add_edges_from(zip([source] * preferential, neighbor_targets))\n",
      "        elif len(neighbors) > 0:\n",
      "             G.add_edges_from(zip([source] * len(neighbors), neighbors))\n",
      "        # Select new targets.\n",
      "        targets = _random_subset(G.nodes(), random)\n",
      "        source += 1\n",
      "    return G\n",
      "\n",
      "\n",
      "def deg_dist(g):\n",
      "    deg_scatter = []\n",
      "    for deg, count in enumerate(nx.degree_histogram(g)):\n",
      "        if count:\n",
      "            deg_scatter.append((deg, count))\n",
      "    return deg_scatter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Degree distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b_a = deg_dist(nx.barabasi_albert_graph(10000, m=4)) # source http://networkx.lanl.gov/_modules/networkx/generators/random_graphs.html#barabasi_albert_graph\n",
      "g25 = deg_dist(simple_hybrid_graph(10000, m=4, alpha=0.25))\n",
      "g50 = deg_dist(simple_hybrid_graph(10000, m=4, alpha=0.50))\n",
      "g75 = deg_dist(simple_hybrid_graph(10000, m=4, alpha=0.75))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter([x[0] for x in b_a], [x[1] for x in b_a], color='green')\n",
      "plt.scatter([x[0] for x in g25], [x[1] for x in g25], color='yellow')\n",
      "plt.scatter([x[0] for x in g50], [x[1] for x in g50], color='blue')\n",
      "plt.scatter([x[0] for x in g75], [x[1] for x in g75], color='red')\n",
      "plt.xscale('log')\n",
      "plt.yscale('log')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wdy+0aQOHDln92WyQlgYbNljPRUSk7jlSsvHggw9G9sjtUaNGMXv2bPbt20eT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\nLCIiIiJig4KziIiIiIgN/x9mJ0rY2aLEzwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x562fe50>"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}