**Social Network**

- 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. Include an image.
- 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.
- Identify a node with high betweenness that you could afford to remove without disconnecting other vertices from that component. Create a second network that excludes that person. Use Net>Transform>Remove>Selected Vertices. Recompute betweenness for everyone remaining in the network. Include an image.
- 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 (if it exists) whose closeness centrality suffers as a result.
- Briefly discuss the ambiguities (& missing data) in this kind of data collection.
- Imagine you are a newcomer who wants to not only be friends with you, but occupy a central position in your network (I know, multiple personality is a bit hard to keep track of). You only have time to make 2 new acquaintances out of your network of friends. 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?).

**Your network vs. random** (bonus)

- 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).
- Select two of your buddies. Look up the value of their individual clustering coefficient in your network.
- 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.
- 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.
- Compute the average clustering coefficient and average shortest path for the corresponding random graph.
- Describe how the clustering coefficient and average shortest path of your social network compare to its random counterpart.
- From this conclude whether or not it exhibits small world properties.

Submission of your homework is via WebCT. You must submit all the required files in a single tar or zip file containing all the files for your submission.

Acknowledgement: The assignment is modified from Lada Adamic.