CS 765: Complex Networks

For this assignment you will use air transportation network data. You may use any of the network analysis tools such as Gephi, NetworkX, graph-tool, Pajek, SNAP, and UCINET. For Gephi, you can import edge and then node files.

1. Who is the most central node in the network by degree, eigenvector, pageRank, closeness, and betweenness?
2. Pick one layout (OpenOrd, Random Layout, etc.) of the network, using the degree as node size and each centrality (eigenvector, pageRank, closeness, and betweenness) as the color vector. Include an image of each with the most central node marked (4 images).
3. Point out 4 vertices whose degree centrality rank differs the most from the other centralities (eigenvector, pageRank, closeness, and betweenness) and explain why it happens. (include marked images)
4. Identify a node with high betweenness that you could remove without disconnecting other vertices from that component. (include marked image) Create a second network that excludes that node. Recompute centralities in the network.
5. Point out 1 particular vertex, whose betweenness centrality rank changed the most (include marked image).
6. Point out 1 particular vertex, whose closeness centrality rank changed the most (include marked image).
7. Point out 1 particular vertex, whose eigenvector centrality rank changed the most (include marked image).
8. Point out 1 particular vertex, whose pageRank centrality rank changed the most (include marked image).
9. Discuss why node in (5) had a change in its betweenness centrality score.
10. Discuss why node in (6) had a change in its closeness centrality score.
11. (bonus) Discuss why node in (7) had a change in its eigenvector centrality score.
12. (bonus) Discuss why node in (8) had a change in its pageRank centrality score.

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