Synchronization and modularity in complex networks

TL;DR

This paper explores how synchronization patterns relate to network modularity in complex systems, revealing a correlation in homogeneous networks but highlighting limitations in networks with hubs.

Contribution

It demonstrates the relationship between synchronization stability and modularity, especially in homogeneous networks, and discusses the impact of hubs on this correlation.

Findings

Stable synchronization patterns correlate with higher modularity in homogeneous networks.

Hubs tend to have high stability but do not improve modularity when isolated.

The correlation between stability and modularity breaks down in networks with hubs.

Abstract

We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the partition these patterns provide. The results indicate that the more stable the patterns are, the larger tends to be the modularity of the partition defined by them. This correlation works pretty well in homogeneous networks (all nodes have similar connectivity) but fails when networks contain hubs, mainly because the modularity is never improved where isolated nodes appear, whereas in the synchronization process the characteristic of hubs is to have a large stability when forming its own community.