Network synchronization: Spectral versus statistical properties

TL;DR

This paper demonstrates that the synchronizability of weighted, possibly asymmetric networks cannot be reliably inferred from their statistical properties, as small structural changes can significantly impact spectral properties crucial for synchronization.

Contribution

The study reveals that standard statistical network metrics do not reliably predict network synchronizability, emphasizing the importance of spectral analysis.

Findings

Statistical properties do not determine synchronizability.

Small structural changes can significantly affect spectral eigenvalues.

Common metrics like degree distribution are insufficient for predicting synchronization.

Abstract

We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks.