Phase synchronization on scale-free networks with community structure

In this Letter, we propose a growing network model that can generate scale-free networks with a tunable community strength. The community strength, C, is directly measured by the ratio of the number of external edges to that of the internal ones; a smaller C   corresponds to a stronger community structure. By using the Kuramoto model, we investigated the phase synchronization on this network and found an abnormal region (C⩽0.002C⩽0.002), in which the network has even worse synchronizability than the unconnected case (C=0C=0). On the other hand, the community effect will vanish when C exceeds 0.1. Between these two extreme regions, a stronger community structure will hinder global synchronization.