Partitioning networks into clusters of synchronized nodes via the message-passing algorithm: an unbiased scalable approach

TL;DR

This paper introduces a scalable message-passing algorithm for partitioning large networks into synchronized clusters, leveraging an Ising-like model to identify coherent groups without spectral analysis, and explores the effects of noise on synchronization transitions.

Contribution

It presents an unbiased, scalable method based on message passing for detecting synchronized clusters, applicable to large real-world networks, and analyzes the impact of noise on synchronization dynamics.

Findings

Abrupt desynchronization occurs even in simple graphs without higher order interactions.

Including noise smooths the transition to synchronization, creating plateaus.

The method effectively identifies synchronized clusters in large networks.

Abstract

Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks. Moreover, within a stochastic framework, it is unclear which dynamics should be chosen to study synchronization. Here we propose an unbiased and scalable method based on the message-passing algorithm. By exploiting the collective behavior emerging across critical points of an effective Ising-like model, we identify dynamically coherent clusters of synchronized nodes and illustrate the approach on some large real-world networks. We find that, unlike continuous-time dynamics, abrupt desyncrhronization occurs even in simple graphs, without the need to invoke higher order interactions. However, when noise is included, the transition to synchronization becomes smoother and proceeds through the formation of plateaus, albeit at the cost of requiring larger coupling strengths.