The course primarily uses two software packages for working with networks, Pajek and Gephi. There are other options and the course forum have seen discussions to which software is better, if the two aforementioned are good enough for the real-world or is only used by academia and so forth. I'll settle with linking to others such as NetworkX and UCINET hoping that I one day will be able to use all of them, but for now I'll focus on Pajek and Gephi to get through the course and perhaps claiming to be more than a novice in networks. Let's get back to the topic of the post, the NFL Super Bowl is this weekend (February 2nd) and even though I'm not an avid follower of American Football it seemed like a fun exercise to visualize the historical Super Bowl matches in a graph. Gephi is useful for manually drawing nodes and edges and this is exactly what I did, many more things can do with Gephi but Pajek which does not have this drawing feature seem to be more geared towards heavy analysis.
The graph have many teams with only one link, meaning the team have only faced one team in the Super Bowl. This is a unweighted graph so it doesn't reveal if the teams that are connected by a link have played each other more than once. It's also clear that there are a few central teams with many links (high degree) which have faced many opponents. This graph is connected (meaning any node is connected to all other nodes through links) but it doesn't have to be. Can you think of how?
Two teams have 6 other unique opponents: New England Patriots, Denver Broncos but there are many more with only one link, as expected. The degree which I mentioned already is empirical to network analysis, and is used in the perhaps simplest measure centrality measure, the degree centrality. Other centrality measures exist, such as closeness centrality, betweenness centrality and eigenvector centrality. Even if these lack any useful meaning in the case of Super Bowl matches, they are commonly used in other graphs and need to be well understood.
This was a trivial analysis and the graph may not be necessary to find out which team that historically faced the most opponents but it was meant to be an introduction to graphs and the Gephi and Pajek software. The files are available for download if anyone wants to extend the data set; for example making it a weighted graph for teams that has played each other more than once, make it directed to embed the winner of a match etc.
https://www.dropbox.com/s/jseiwvdclp7qe9j/super%20bowl%20graph.gephi
https://www.dropbox.com/s/1jl161340renfkv/super%20bowl%20graph.net
