Structural Analysis and Visualization of Networks

Home Assignment #1: Power law

Student: *{Your Name}*

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General Information

Due Date: 28.01.2015 23:59 <br > Late submission policy: -0.2 points per day <br >

Please send your reports to mailto:[email protected] and mailto:[email protected] with message subject of the following structure:<br > [HSE Networks 2015] {LastName} {First Name} HA{Number}

Support your computations with figures and comments. <br > If you are using IPython Notebook you may use this file as a starting point of your report.<br > <br >

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Problems

Task 1.

Load wordcounts dataset.

1. Check that Zipf's Law holds
2. Assuming that the data is distributed according to the Power Law, find
   • $\alpha$ of the distribution
   • mean sample variance $\sigma^2$
3. Produce summary of the frequencies: min, max, mean, median

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Task 2.

Find and plot PDF and CDF for the following networks:

• Routing network
• Web graph
• Facebook network

1. Are they correspondent to power law?
2. Find max and mean values of incoming and outcoming node degrees
3. Find $\alpha$ via Maximum Likelihood and calculate $\sigma^2$
4. Determine $x_{min}$ via Kolmogorov-Smirnov test

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