CS 765: Complex Networks

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 -left one) and (b -right one) in :
(a): The corresponding adjacency matrices.
(b): The corresponding link lists.
(c): Determine the average clustering coefficient of the network shown in (a)

Bipartite Graphs (5 points)

• Download the 2-mode actors and movies data.
• Download the 1-mode actors and movies data.
• Open it in Gephi, data is edgelist format, and separated with tab.
• This is a 2 mode network containing two classes of nodes, actors and movies, and 1 mode projection of 2 mode network.

1. Visualize the 2-Mode network. The two classes of nodes should be colored differently. If labels are not shown, add them. Include an image of layout.
2. Visualize the 1-Mode network. If labels are not shown, add them. Include an image of layout.
3. Qualitatively compare the structure of the 2-Mode to the 1-Mode network of actors. Is there a loss of information?
4. In 1-Mode network, show the weights on each edge. What do the values represent?
5. In 1-Mode network, compute the unweighted degree of each node. What does degree represent?
6. In 2-Mode network, make node size proportional to degree. Include an image.
7. Who are the most important actors using degree centrality?
8. Remove all edges between actors who have costarred in fewer than 3 movies. Include an image of layout.

Submission of your homework is via WebCampus. You must submit all the required files in a single pdf document containing all the answers.