# CS 765 Complex Networks

## Due on Thursday Mar 14, 2013 at 1:00 pm

PageRank (4 points)

Construct a small directed network (about 10 nodes) in GDF or .net format and load it into GUESS. Construct it such that you have at least one node that will have low indegree but high PageRank

1. Compute the PageRank of each node by typing `g.nodes.pagerank`
2. Color by PageRank `colorize(pagerank,green,yellow)`
3. Compute the indegree `g.nodes.indegree`
4. Size the nodes by indegree `resizeLinear(indegree,minsize,maxsize)` (you are choosing minsize and maxsize)
5. Turn in an image of your network.
6. Point out a node that has high PageRank but low indegree. Explain qualitatively how this came about.

an aside: You can also use the GUESS toolbar pageranktoolW.py, if you'd like to see how the algorithm converges.

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.