Modular synchronization in complex networks with a gauge Kuramoto model

TL;DR

This paper introduces a gauge-modified Kuramoto model that leverages edge betweenness centrality to identify modular structures in complex networks through phase synchronization patterns.

Contribution

The study presents a novel gauge term in the Kuramoto model that efficiently detects modules in complex networks based on synchronization behavior.

Findings

The gauge Kuramoto model successfully distinguishes modules within networks.

The method requires only L computational complexity, making it efficient.

Comparison shows differences in synchronization patterns between the modified and original models.

Abstract

We modify the Kuramoto model for synchronization on complex networks by introducing a gauge term that depends on the edge betweenness centrality (BC). The gauge term introduces additional phase difference between two vertices from 0 to $\pi$ as the BC on the edge between them increases from the minimum to the maximum in the network. When the network has a modular structure, the model generates the phase synchronization within each module, however, not over the entire system. Based on this feature, we can distinguish modules in complex networks, with relatively little computational time of $\mathcal{O}(NL)$, where $N$ and $L$ are the number of vertices and edges in the system, respectively. We also examine the synchronization of the modified Kuramoto model and compare it with that of the original Kuramoto model in several complex networks.