Community structure in real-world networks from a non-parametrical synchronization-based dynamical approach

TL;DR

This paper presents a non-parametric, synchronization-based dynamical approach using adaptive coupled chaotic oscillators to detect community structures in real-world networks, demonstrating that frequency adaptation reveals underlying communities.

Contribution

It introduces a parameterless frequency adaptation mechanism in synchronization dynamics to uncover community structures without prior parameters.

Findings

Frequency vector reveals community structure

Adaptive mechanism enhances stability of synchronized states

Method applicable to real-world networks

Abstract

This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic R\"{o}ssler oscillators each one characterized by a defined natural frequency, and coupled according to a predefined network topology. The interaction scheme contemplates an uniformly increasing coupling force to simulate a society in which the association between the agents grows in time. To enhance the stability of the correlated states that could emerge from the synchronization process, we propose a parameterless mechanism that adapts the characteristic frequencies of coupled oscillators according to a dynamic connectivity matrix deduced from correlated data. We show that the characteristic frequency vector that results from the adaptation mechanism reveals the underlying community structure present in the network.