# CS 765 Complex Networks

## Fall 2016

## Network Lab 4

## Due on Wednesday Nov 1, 2017 at 1 pm

**Power-law network**
Using any programming language, generate 100,000 random integers from a power law distribution with exponent alpha = 2.1. Note that the slides #90-105 discuss the power law generation and fitting.

- What is the largest value in your sample?
Is it possible for a node in a network to have a degree this high (assuming you don't allow multiple edges between two nodes)?
- Construct a histogram of the frequency of occurrence of each integer in your sample.
Try both a linear scale plot and a log-log scale plot. (include snapshots)
- What happens to the bins with zero count in the log-log plot?
- Try a simple linear regression on the log transformation of both variables.
(In Matlab, you can plot two data sets together as follows:
`plot(x1,y1,'r-',x2,y2,'b:')`.
This will plot y1 vs. x1 as a red solid line, and y2 vs. x2 as a blue dotted line.)
What is your value of the power-law exponent alpha? Include a plot of the data with the fit superimposed.
- Now exponentially bin the data and fit with a line. What is your value of alpha?
- Do a cumulative frequency plot of the original data sample. Fit, plot, and report on the fitted exponent and the corresponding value of alpha.
- Finally, do a maximum likelihood fitting of the data. Plot the results and report the alpha.
- Which method was the most accurate? Which one, in your opinion, gave the best view of the data and the fit?

**Submitting your files**
Submission of your homework is via WebCampus.
You must submit all the required files in a single pdf document containing all the answers.

Acknowledgement: The assignment is modified from Lada Adamic.