# CS 765: Complex Networks

## Due on Monday Sep 17 at 2 pm

Network Basics (2 points)

Go to the site http://www.visualcomplexity.com. Select and list two projects describing a network. Answer the following about them (this may require going into the source webpage for the project, linked to from the visualcomplexity site).

1. What do the nodes and edges represent?
2. Is the graph directed? Weighted?
3. Can the data be represented as a bipartite graph?

Complete 2.12.3: Graph Representation (3 points)
The adjacency matrix is a useful graph representation for many analytical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Image 2.20:
(c): Determine the average clustering coefficient of the network shown in Image 2.20a.

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?