# CS 765 Complex Networks

## Due on Tuesday Oct 28, 2014 at 9:30 am

Your network vs. random (4 points)

For this lab, you will need to use your Facebook network from 2nd lab

1. Compute the average clustering coefficient (Net>Vector>Clustering Coefficients>CC1) and average shortest path (Net>Paths between two vertices > Distribution of distances > From all vertices and look in the report window).
2. Select two of your buddies. Look up the value of their individual clustering coefficient in your network.
3. Highlight their ego-networks (just them and their friends) and explain the clustering coefficient in terms of their number of friends (well, their number of their friends who are also your friends) and the number of edges they have between them.
4. Construct a random network with the same number of nodes and average degree (Net>Random Network>Erdos-Renyi>undirected). Visualize it and include an image.
5. Compute the average clustering coefficient and average shortest path for the corresponding random graph.
6. Describe how the clustering coefficient and average shortest path of your social network compare to its random counterpart.
7. From this conclude whether or not it exhibits small world properties. (bonus)
Random graphs and giant components (2 points)
1. Go to http://ccl.northwestern.edu/netlogo/models/GiantComponent and launch the applet. Click 'setup' and then 'go'.

2. Try it with 80 nodes and then 400 (if your computer can not compute, use smaller node sizes). Observe what happens right around the point where the average degree is 1 (the vertical line in the plot). Comment about the variation in the size of the largest component as you increase the number of edges/nodes.
Growing networks: preferential and random growth (4 points)

Open the NetLogo applet: Click on 'setup' to start out with a cycle of 5 vertices. Click on 'go-once' to add vertices one by one, each with m edges. Play with the m and gamma parameters.

1. Select m=1 and gamma=0. Add 300 vertices. Click on the 'resize nodes' button to size the vertices by their degree. Repeat the same, but with m = 1 and gamma = 1. What differences do you observe between the two networks, e.g. in terms of appearance, the number of vertices with degree 1, and the maximum degree of any vertex?
2. Generate two networks with 1000 vertices and m = 4. (You can run this faster by adjusting the speed slider at the top.) For one network select gamma = 0, and for the other gamma = 1. Which degree distribution looks more like a power law?