CS 765 Complex Networks

Go to Giant Component. Click 'setup' and then 'go'.

1. Try it with 80 nodes and then 500 nodes. Observe what happens right around the point where the average degree is 1 (the vertical line in the plot). Comment about how fraction of nodes in giant component change?

Open the Preferential Attachment: Click on 'setup' to start out with a cycle of 2 vertices. Click on 'go-once' to add vertices one by one, each with 1 edge.

1. Generate a networks with 500 vertices. (You can run this faster by adjusting the speed slider at the top.) Include a snapshot. Around when did you see a power-law degree distribution?

Go to Small Worlds. Try different rewiring probabilities ranging from 0 to 1. By clicking on rewire-one multiple times you can see how the average path length and clustering coefficient change each time rewiring happens.

1. Discuss for which probability value we can obtain small world network. Include a snapshot.

1. (2 points) Using any programming language, generate 100,000 random integers from a power law distribution with exponent alpha = 2.1.
2. (1 point) 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)?
3. (1 point) 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)
4. (1 point) What happens to the bins with zero count in the log-log plot?

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