Laplacian Dynamics and Multiscale Modular Structure in Networks

TL;DR

This paper introduces a dynamic, multiscale approach to community detection in networks using Laplacian-based stability measures, unifying existing methods and enabling efficient analysis of large networks.

Contribution

It presents a novel stability measure based on Laplacian dynamics that captures community structures at multiple resolutions, extending and unifying existing community detection techniques.

Findings

The stability measure generalizes modularity and spectral methods.

Multi-scale community structures can be identified efficiently.

The approach applies to large networks with extended algorithms.

Abstract

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.