Generalized modularity for community detection

Detecting the underlying community structure of networks is an important problem in complex network analysis. Modularity is a well-known quality function introduced by Newman, that measures how vertices in a community share more edges than what would be expected in a randomized network. However, this limited view on vertex similarity leads to limits in what can be resolved by modularity. To overcome these limitations, we propose a generalized modularity measure called GM which has a more sophisticated interpretation of vertex similarity. In particular, GM also takes into account the number of longer paths between vertices, compared to what would be expected in a randomized network. We also introduce a unified version of GM which detects communities of unipartite and (near-)bipartite networks without knowing the structure type in advance. Experiments on different synthetic and real data sets, demonstrate GM performs strongly in comparison to several existing approaches, particularly for small-world networks.