Synchronization interfaces and overlapping communities in complex networks

TL;DR

This paper investigates interfaces between synchronized domains in complex networks of phase oscillators, providing a new method to identify overlapping communities and their dynamics within modular networks.

Contribution

It introduces a framework for understanding interfaces in synchronized networks and offers an algorithm to detect overlapping nodes and clusters.

Findings

Interfaces can form between synchronized domains in phase oscillator networks.

The method identifies overlapping nodes and clusters in modular networks.

Results provide a functional definition of overlapping structures.

Abstract

We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied in the general framework of interacting phase oscillators composed of either dynamical domains (influenced by different forcing processes), or structural domains (modular networks). The obtained results allow to give a functional definition of overlapping structures in modular networks, and suggest a practical method to identify them. As a result, our algorithm could detect information on both single overlapping nodes and overlapping clusters.