# CS 765 Complex Networks

## Due on Wednesday Sep 27, 2017 at 1 pm

Bipartite Graphs (5 points)

For this part, you may look at Pajek tutorial.

• Open it in Pajek. A report window should pop up confirming that the graph has been read.
• This is a 2 mode network containing two classes of nodes, actors and movies. Create a 2-mode partition.
1. Visualize the network. The two classes of nodes should be colored differently. If labels are not shown, add them. Include an image of layout.
2. Transfrom the network into a one-mode network. Include an image.
3. Qualitatively compare the structure of the 2-Mode to the 1-Mode network of actors. Is there a loss of information?
4. Show the weights on each edge. What do the values represent?
5. Compute the unweighted degree of each node. How is the degree represented?
6. Add the vector value to each vertex (it will be the degree/(max possible degree)). Include an image.
7. Who are the most important actors using degree centrality?
8. How does the boundary of the network (i.e. who is included) affect who is found to be most central?
9. Load the file actorsandmoviesWithGere.net. It contains one extra actor, Richard Gere. Repeat the above procedure.
10. In the 1-mode network of actors, is there a change in who is most central?
11. What does this tell you about biases and boundaries in sample selection?
12. Remove all edges between actors who have costarred in fewer than 3 movies. Which actors comprise the central core of this network?

Social Network (5 points)

For this assignment you will use friend circle data.

1. Do an energy layout of the network, using the degree partition and either closeness or betweenness as the vector. Include an image.
2. Who is the most central node in the network by degree, closeness and betweenness?
3. 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.
4. 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. Recompute betweenness for everyone remaining in the network. Include an image.
5. Point out 2 particular vertices and their position in the network. Discuss why their betweenness centrality score did or did not change.
6. Point out 1 vertex (if it exists) whose closeness centrality suffers as a result.
7. Imagine you are a newcomer who wants to not only be friends with you, but occupy a central position in your network. 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?
8. Add yourself to the network and compute your closeness (or you could alter the data file). Which 2 vertices would you connect to to maximize your betweenness score (what is your betweenness?).