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  {

   "cells": [

    {

     "cell_type": "heading",

     "level": 1,

     "metadata": {},

     "source": [

      "Network Models: Random Graphs"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import numpy as np\n",

      "import matplotlib.pyplot as plt\n",

      "plt.xkcd()\n",

      "import networkx as nx\n",

      "%matplotlib inline"

     ],

     "language": "python",

     "metadata": {},

     "outputs": []

    },

    {

     "cell_type": "heading",

     "level": 3,

     "metadata": {},

     "source": [

      "Clustering coefficient"

     ]

    },

    {

     "cell_type": "markdown",

     "metadata": {},

     "source": [

      "During the lecture we have understood, that the clustering coefficient of a random graph is equal to the probability $p$: $$\\text{Clustering coefficient} = \\frac{\\langle k \\rangle}{n} = p $$\n",

      "\n",

      "In this task you have to check it on generated data.\n",

      "Please, generate $100$ Random Graphs with $n = 1000$ and $p = 0.002$ (for saving computational time) and plot the box-plot of your computations."

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "# Put your code here"

     ],

     "language": "python",

     "metadata": {},

     "outputs": []

    },

    {

     "cell_type": "heading",

     "level": 3,

     "metadata": {},

     "source": [

      "Size of small components"

     ]

    },

    {

     "cell_type": "markdown",

     "metadata": {},

     "source": [

      "In this task you are asked to calculate the average size of small components (small component = not a giant one) with regard to average degree of the network. To see the effect clearly, plot average size around $\\langle k \\rangle = 1$."

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "# Put your code here"

     ],

     "language": "python",

     "metadata": {},

     "outputs": []

    }

   ],

   "metadata": {}

  }

 ]

}