1. Centrality
Download the file v3.net from cTools. This data set was extracted from the class survey where students reported who they were acquainted with prior to the class. Although initially directed, the edges are undirected in this version.

• Do an energy layout of the network using the Draw>Draw-Partition-Vector command, using the degree partition and either closeness or betweenness as the vector (*I*). Who is the most central node in the network by degree, closeness and betweenness?
• Point out 3 vertices whose centrality scores differ (e.g. high betweenness but medium closeness) and explain from their position in the network why it happens.
• In the first week, Jude was still out of town and did not fill out the survey (and other people didn't see him in the class, so they didn't list him in their responses). Roll back time and create a second network that excludes him (sorry Jude!). Use Partition>Null Partition to create a single partition of value '0'. Now click on the edit icon next to the partition and put a '1' next to Jude's name. Next, create a new network that excludes him by selecting Operations>Extract from network>Partition and selecting the '0' partition.
• Recompute betweenness for everyone remaining in the network.
• Point out 2 particular vertices and their position in the network discuss why their betweenness centrality score did or did not change.
• Point out 1 vertex whose closeness centrality was particularly positively impacted by Jude's arrival.
• Briefly discuss the shortcomings of this particular data collection method, and how those shortcomings could affect centrality measurements.
• Imagine you are a newcomer to the class. You only have time to make 2 new acquaintances. Which 2 would you choose to maximize your closeness centrality? Add yourself to the network by using the command Net>Transform>Add>Vertices and adding edges in the Draw window and compute your closeness. Which 2 vertices would you connect to to maximize your betweenness score (what is your betweenness?).

2. Prestige and the adoption of new practices
Complete assignment 9.9 in the prestige chapter of "Exploratory Social Network Analysis with Pajek". You can download the data from http://vlado.fmf.uni-lj.si/pub/networks/data/esna/Galesburg2.htm or as a project file from cTools.

3. Eigenvector prestige

Construct a transition matrix for the above network. Let the teleportation probability be 0. Use Matlab (or another method of your choice) to find the stationary distribution given by the eigenvector corresponding to the eigenvalue lambda = 1 of the transpose of your transition matrix. Normalize the eigenvector so that it represents the probabilities of the random walker to be at any given vertex. Next, use the iterative method to derive the same result starting with a uniform vector (also appropriately normalized). How many iterations does it take for the norm of the difference of the two vectors to be less than 0.01?