Demo analysis of KONECT's Internet topology network dataset ... (dataset from 2015, updated by me, IPv4 only!) http://irl.cs.ucla.edu/topology/

notebook2-topology-2015.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pandas as pd\n",
      "from scipy import stats, integrate\n",
      "import matplotlib.pyplot as plt\n",
      "from operator import mul\n",
      "import requests\n",
      "import re\n",
      "\n",
      "from graph_tool.all import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Load Dataset"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "NETWORK_NAME = 'topology' # arenas-pgp, topology, as20000102"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# g = graph_tool.collection.konect_data[NETWORK_NAME] \n",
      "g = graph_tool.collection.load_koblenz_dir('topology2') \n",
      "# print g.gp.readme"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<Graph object, undirected, with 49448 vertices and 212543 edges at 0x7f448dbc71d0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = requests.get('http://konect.uni-koblenz.de/networks/' + NETWORK_NAME).text\n",
      "print re.search('description\">(.*)</div></div>', r).group(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "This is the network of connections between autonomous systems of the Internet. The nodes are autonomous systems (AS), i.e. collections of connected IP routing prefixes controlled by independent network operators. Edges are connections between autonomous systems. Multiple edges may connect two nodes, each representing an individual connection in time. Edges are annotated with the timepoint of the connection.\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Helper Functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_hist(data, xlog=False, ylog=True, label=''):\n",
      "    plt.bar(range(len(data[0])), data[0], log=ylog)\n",
      "    if xlog:\n",
      "        plt.xscale('log')\n",
      "    plt.title(label + ' Histogram')\n",
      "    plt.xlabel(label)\n",
      "    plt.ylabel('Frequency')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def avg_from_hist(data):\n",
      "    ammount = data[0]\n",
      "    label = data[1][:-1]\n",
      "    return sum(map(mul, ammount, label)) / sum(ammount)\n",
      "\n",
      "# for degrees, this is equal to vertex_average(g, 'total')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Shortest-distance\n",
      "the shortest-distance for each vertex pair in the graph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_hist = distance_histogram(g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_hist(distance_hist, label='Shortest Distance')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JTTAiItYxlabVdo5VQNUVNaPukyd6eluXI0xcpK65Jn7iJ35v4k/sZ0Mv4/f+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\nmt+yVz4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fba3cac9f90>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Average Shortest-distance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "avg_from_hist(distance_hist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "3.747064003366638"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Degree\n",
      "the vertex degree."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "degree_hist = vertex_hist(g, \"total\")\n",
      "# degree_hist"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_hist(degree_hist, label='Degree')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fba48149bd0>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_hist(degree_hist, xlog=True, label='Degree')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QJLViwJAktWLAkCS18v8B/Ey1JlzObeYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fba47c71610>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Average Degree"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "avg_from_hist(degree_hist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "8.5966267594240406"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vertex_average(g, 'total')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "(8.59662675942404, 0.2892062692872614)"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    }
   ],
   "metadata": {}
  }
 ]
}