Synchronization in clustered random networks

TL;DR

This paper investigates how clustering affects synchronization in random networks of Kuramoto oscillators, finding that small cycles do not significantly influence synchronization, which can be accurately modeled by tree-based theories.

Contribution

It demonstrates that cycles of order three are negligible for synchronization, allowing tree-based models to predict behavior in highly clustered networks.

Findings

Cycles of order three do not significantly impact synchronization.

Tree-based theories accurately predict synchronization in clustered networks.

Numerical simulations confirm theoretical predictions.

Abstract

In this paper we study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order three does not play an important role on network synchronization, showing that the synchronization of random clustered networks can be described by tree-based theories, even for high values of clustering. In order to support our findings, we provide numerical simulations considering clustered and non-clustered networks, which are in good agreement with our theoretical results.