00_01._networks_ha1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Network Science</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center>Home Assignment #1: Power law</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <center>Student: *{Your Name}*</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <hr /> General Information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Due Date:** 08.02.2016 23:59 <br \\>\n",
    "**Late submission policy:** -0.2 points per day <br \\>\n",
    "\n",
    "\n",
    "Please send your reports to <mailto:network.hse.2016@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": "markdown",
   "metadata": {},
   "source": [
    "## Problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load [wordcounts](http://www.leonidzhukov.net/hse/2015/networks/data/wordcounts.txt) dataset. \n",
    "1. Check that Zipf's Law holds\n",
    "2. Assuming that the data is distributed according to the Power Law, find\n",
    " * $\\alpha$ of the distribution\n",
    " * mean sample variance $\\sigma^2$\n",
    "3. Produce summary of the frequencies: min, max, mean, median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Start your code here\n",
    "#\n",
    "#\n",
    "#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <hr /> Task 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find and plot PDF and CDF for the following networks:\n",
    "* [Routing network](http://www.leonidzhukov.net/hse/2015/networks/data/network.txt)\n",
    "* [Web graph](http://www.leonidzhukov.net/hse/2015/networks/data/web_Stanford.txt)\n",
    "* [Facebook network](http://www.leonidzhukov.net/hse/2015/networks/data/fb_Princeton.txt)\n",
    "\n",
    "\n",
    "1. Are they correspondent to power law?\n",
    "2. Find max and mean values of incoming and outcoming node degrees\n",
    "3. Find $\\alpha$ via Maximum Likelihood and calculate $\\sigma^2$\n",
    "4. Determine $x_{min}$ via Kolmogorov-Smirnov test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Start your code here\n",
    "#\n",
    "#\n",
    "#"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}