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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "<center>Structural Analysis and Visualization of Networks</center>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "<center>Home Assignment #2: Network models</center>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "<center>Student: *{Your Name}*</center>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "<hr />\n",
      "General Information"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Due Date:** 18.02.2015 23:59 <br \\>\n",
      "**Late submission policy:** -0.2 points per day <br \\>\n",
      "\n",
      "\n",
      "Please send your reports to <mailto:leonid.e.zhukov@gmail.com> and <mailto:shestakoffandrey@gmail.com> with message subject of the following structure:<br \\> **[HSE Networks 2015] *{LastName}* *{First Name}* HA*{Number}***\n",
      "\n",
      "Support your computations with figures and comments. <br \\>\n",
      "If you are using IPython Notebook you may use this file as a starting point of your report.<br \\>\n",
      "<br \\>\n",
      "<hr \\>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problems"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Task 1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider Barabasi and Albert dynamical grow model. Two main ingredients of this model are *network growing* and *prefferential attachment*. Implement two restricted B&A-based models:\n",
      "<br \\>\n",
      "\n",
      "**Model A**\n",
      "<br \\>\n",
      "Lack of prefferential attachment, that is at each time-step form edges uniformly at random while network keeps growing.\n",
      "\n",
      "**Model B**\n",
      "<br \\>\n",
      "Lack of growing, that is fix total number of nodes, on each time-step randomly choose one and form edges with prefferential attachment.\n",
      "<br \\>\n",
      "\n",
      "1. Generate networks according to the models above ($N > 1000$ nodes)\n",
      "2. Compute CDF/PDF, describe the distribution and compute\\describe its properties.\n",
      "3. Illustate the following dependencies: \n",
      "    * average path length to the number of nodes\n",
      "    * average clustering coefficient to the number of nodes\n",
      "    * average node degee to the nodes \"age\"\n",
      "4. Is scale-free property conserved in these models?\n",
      "\n",
      "Analyse results with respect to various parameter settings"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "<hr />\n",
      "Task 2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider the following  \"Vertex copying model\" of growing network.\n",
      "\n",
      "At every time step a random vertex from already existing vertices is selected and duplicated together with all edges, such that  every edge of the  vertex\n",
      "* is copied with probability $q$\n",
      "* is rewired to any other randomly selected vertex with probability $1-q$\n",
      "\n",
      "\n",
      "Starting state is defined by some small number of randomly connected vertices.\n",
      "\n",
      "The model can generate both directed and undirected networks.\n",
      "\n",
      "1. Generate  graphs based on the model ($N > 1000$ nodes)\n",
      "2. Compute CDF/PDF, describe the distribution and compute\\describe its properties.\n",
      "3. Illustate the following dependencies: \n",
      "    * average path length to the number of nodes\n",
      "    * average clustering coefficient to the number of nodes\n",
      "    * average node degee to the nodes \"age\"\n",
      "    \n",
      "Analyse results with respect to various parameter settings"
     ]
    }
   ],
   "metadata": {}
  }
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}