By the way, there are several other modularity variants that all differ in the null model being used; for instance, a directed modularity measure was proposed by Kim et al based on using the PageRank vectors instead of the degrees. There's also a Laplacian formulation of modularity by Lambiotte, Delvenne and Barahona: http://arxiv.org/abs/0812.1770. We might want to adapt the modularity function completely so it can take different null models.
By the way, there are several other modularity variants that all differ in the null model being used; for instance, a directed modularity measure was proposed by Kim et al based on using the PageRank vectors instead of the degrees. There's also a Laplacian formulation of modularity by Lambiotte, Delvenne and Barahona: http:// arxiv.org/ abs/0812. 1770. We might want to adapt the modularity function completely so it can take different null models.