CS 765: Complex Networks
Network Lab 1
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).
- What do the nodes and edges represent?
- Is the graph directed? Weighted?
- 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:
(a): The corresponding adjacency matrices.
(b): The corresponding link lists.
(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.
- Download the file actorsandmovies.net
- 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.
Submitting your files
- Visualize the network. The two classes of nodes should be colored differently. If labels are not shown, add them. Include an image of layout.
- Transfrom the network into a one-mode network. Include an image.
- Qualitatively compare the structure of the 2-Mode to the 1-Mode network of actors. Is there a loss of information?
- Show the weights on each edge. What do the values represent?
- Compute the unweighted degree of each node. How is the degree represented?
- Add the vector value to each vertex (it will be the degree/(max possible degree)). Include an image.
- Who are the most important actors using degree centrality?
How does the boundary of the network (i.e. who is included) affect who is found to be most central?
- Load the file actorsandmoviesWithGere.net. It contains one extra actor, Richard Gere. Repeat the above procedure.
- In the 1-mode network of actors, is there a change in who is most central?
What does this tell you about biases and boundaries in sample selection?
- Remove all edges between actors who have costarred in fewer than 3 movies. Which actors comprise the central core of this network?
Submission of your homework is via WebCampus.
You must submit all the required files in a single pdf document containing all the answers.