Looking beyond community structure leads to the discovery of dynamical communities in weighted networks

Abstract

A fundamental question is whether groups of nodes of a complex network can possibly display long-term cluster-synchronized behavior. While this question has been addressed for the restricted classes of unweighted and labeled graphs, it remains an open problem for the more general class of weighted networks. The emergence of coordinated motion of nodes in natural and technological networks is directly related to the network structure through the concept of an equitable partition, which determines which nodes can show long-term synchronized behavior and which nodes cannot. We provide a method to detect the presence of nearly equitable partitions in weighted networks, based on minimal information about the network structure. With this approach we are able to discover the presence of dynamical communities in both synthetic and real technological, biological, and social networks, to a statistically significant level. We show that our approach based on dynamical communities is better at predicting the emergence of synchronized behavior than existing methods to detect community structure.