Relations between Average Distance, Heterogeneity and Network Synchronizability

TL;DR

This paper explores how average distance and degree heterogeneity affect network synchronizability, revealing that shorter average distances and uniform degree distributions enhance synchronization, challenging the sole reliance on maximal betweenness as an indicator.

Contribution

It demonstrates the combined influence of average distance and degree heterogeneity on synchronizability, providing a nuanced understanding beyond maximal betweenness.

Findings

Shorter average distance improves synchronizability.

Lower degree heterogeneity enhances network synchronization.

Maximal betweenness alone may not fully predict synchronizability.

Abstract

By using the random interchanging algorithm, we investigate the relations between average distance, standard deviation of degree distribution and synchronizability of complex networks. We find that both increasing the average distance and magnifying the degree deviation will make the network synchronize harder. Only the combination of short average distance and small standard deviation of degree distribution that ensures strong synchronizability. Some previous studies assert that the maximal betweenness is a right quantity to estimate network synchronizability: the larger the maximal betweenness, the poorer the network synchronizability. Here we address an interesting case, which strongly suggests that the single quantity, maximal betweenness, may not give a comprehensive description of network synchronizability.