Clustering and Synchronization of Oscillator Networks

TL;DR

This paper investigates how clustering affects synchronization in oscillator networks, revealing that increased clustering hampers global synchronization but can enhance hub synchronization in scale-free networks, with implications for brain dynamics.

Contribution

It introduces a method to manipulate clustering without changing degree distribution and studies its effects on synchronization in different network types.

Findings

Increased clustering hinders global synchronization.

Clustering promotes synchronization of hubs in scale-free networks.

Scale-free networks exhibit an additional synchronization transition.

Abstract

Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, scale-free networks show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain with its scale-free and highly clustered structure.