Modular synchronization in complex networks

TL;DR

This paper investigates how different types of inter-modular connections in complex networks influence the synchronization transition, revealing distinct behaviors in decentralized versus centralized structures and providing scaling analysis results.

Contribution

It introduces a modified Kuramoto model on modular networks and demonstrates how inter-modular connection types affect synchronization, with empirical and artificial network analyses.

Findings

Synchronization transition depends on inter-modular connection type.

Decentralized connections lead to finite coupling transition; centralized connections behave abnormally.

Scaling exponent differs from mean-field predictions in modular networks.

Abstract

We study the synchronization transition (ST) of a modified Kuramoto model on two different types of modular complex networks. It is found that the ST depends on the type of inter-modular connections. For the network with decentralized (centralized) inter-modular connections, the ST occurs at finite coupling constant (behaves abnormally). Such distinct features are found in the yeast protein interaction network and the Internet, respectively. Moreover, by applying the finite-size scaling analysis to an artificial network with decentralized inter-modular connections, we obtain the exponent associated with the order parameter of the ST to be $\beta \approx 1$ different from $\beta_{\rm MF} \approx 1/2$ obtained from the scale-free network with the same degree distribution but the absence of modular structure, corresponding to the mean field value.