Demo analysis of KONECT's Internet topology network dataset ... (dataset from 2005)

notebook2-topology.ipynb

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 "worksheets": [
  {
   "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] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "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": 6
    },
    {
     "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": 7
    },
    {
     "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": 8
    },
    {
     "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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mlDrg+3C8xsVr3nfF8Zodqxvita+iEsRmTQiuZx6vmZkNTVEDwavZMBhNur+q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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe5926eb290>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "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": 10,
       "text": [
        "3.7678760610552895"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "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": 11
    },
    {
     "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 0x7fe57047da90>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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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Ozz4wmfFdAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe571f37890>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "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": 14,
       "text": [
        "9.8617991427174125"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vertex_average(g, 'total')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(9.861799142717413, 0.44994352911405905)"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}