RT Journal Article
SR Electronic
T1 Scalable detection of statistically significant communities and hierarchies, using message passing for modularity
JF Proceedings of the National Academy of Sciences
JO Proc Natl Acad Sci USA
FD National Academy of Sciences
DO 10.1073/pnas.1409770111
A1 Zhang, Pan
A1 Moore, Cristopher
YR 2014
UL http://www.pnas.org/content/early/2014/12/04/1409770111.abstract
AB Most work on community detection does not address the issue of statistical significance, and many algorithms are prone to overfitting. We address this using tools from statistical physics. Rather than trying to find the partition of a network that maximizes the modularity, our approach seeks the consensus of many high-modularity partitions. We do this with a scalable message-passing algorithm, derived by treating the modularity as a Hamiltonian and applying the cavity method. We show analytically that our algorithm succeeds all the way down to the detectability transition in the stochastic block model; it also performs well on real-world networks. It also provides a principled method for determining the number of groups or hierarchies of communities and subcommunities.Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory ‘‘communities’’ in random graphs where none exist. We address this problem by using the modularity as a Hamiltonian at finite temperature and using an efficient belief propagation algorithm to obtain the consensus of many partitions with high modularity, rather than looking for a single partition that maximizes it. We show analytically and numerically that the proposed algorithm works all of the way down to the detectability transition in networks generated by the stochastic block model. It also performs well on real-world networks, revealing large communities in some networks where previous work has claimed no communities exist. Finally we show that by applying our algorithm recursively, subdividing communities until no statistically significant subcommunities can be found, we can detect hierarchical structure in real-world networks more efficiently than previous methods.