Multiscale Community Mining in Networks Using Spectral Graph Wavelets

TL;DR

This paper introduces a multiscale community detection method in networks using spectral graph wavelets, enabling identification of community structures at different scales based on scale-dependent information.

Contribution

It develops a novel approach leveraging graph wavelets for multiscale community mining, including new practical tools and scale-dependent modularity for complex networks.

Findings

Successfully identifies hierarchical community structures.

Effective in estimating multiscale community boundaries.

Demonstrates applicability on benchmark networks.

Abstract

For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description is proposed in which community structures are identified at different scales. To this end, we take advantage of the local and scale-dependent information encoded in graph wavelets. After new developments for the practical use of graph wavelets, studying proper scale boundaries and parameters and introducing scaling functions, we propose a method to mine for communities in complex networks in a scale-dependent manner. It relies on classifying nodes according to their wavelets or scaling functions, using a scale-dependent modularity function. An example on a graph benchmark having hierarchical communities shows that we estimate successfully its multiscale structure.