Go to PageRank.
After '`setup`' with 1 random surfer you'll see a small network. By clicking on the '`step`' button, you will be calculating the PageRank of each node.
It will take several iterations for the algorithm to converge.
At each iteration, the probability that a random walker is found at any given node A is proportional to the
probability that it was on a node B with a directed edge to A, divided by the outdegree of node B.
The edge width in the visualization is proportional to the probability that a node transitions from B to A.

- Approximately how many iterations does the algorithm take to converge?
- Try increasing the damping factor (teleportation probability). How does this influence the PageRanks assigned to the nodes?

**PageRank** (2 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

- Compute the PageRank of each node by typing
`g.nodes.pagerank`

. Color by PageRank`colorize(pagerank,green,yellow)`

. - Compute the indegree
`g.nodes.indegree`

. Size the nodes by indegree`resizeLinear(indegree,minsize,maxsize)`

(you are choosing minsize and maxsize). Turn in an image of your network.

- Go to Giant Component. Click 'setup' and then 'go'.
- Try it with 80 nodes and then 500 (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.

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.

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

Go to Small Worlds. This is a NetLogo model that will allow you to vary the rewiring probability.

- Adjust this probability from 0 to 1, each time hitting "rewire" and allowing it to calculate the clustering coefficient and average path length. Does your plot agree with what you saw in lecture?
- In what ways do the random links make the world smaller?

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.