Hi, I'm working on a project which involves analysing thousands of networks, trying to identify those networks that might exhibit communities. Some of these graphs have more than 10,000 edges and I was wondering whether anybody on the list has dealt with large graphs and any strategies they may have employed. I'm using igraph via the R interface.
On a related note, while I've been using the modularity function to get a single number characterizing the presence of communities, I've also been looking at the betweeness of individual nodes. The thing I notice is that in many cases, the modularity is pretty low, but the difference between the average betweeness of the nodes and maximum betweenness is very high. This suggests that one of the nodes is acting like a 'bridge' - would this be a reasonable way to consider the presence of groups in a network, either in addition to the modularity value or inspite of a low modularity value?