Spectral methods for the detection of network community structure: a comparative analysis

TL;DR

This paper compares various spectral methods for detecting community structures in networks, finding that the normalized Laplacian and correlation matrices outperform others, highlighting the importance of considering node degree heterogeneity.

Contribution

It provides a comparative analysis of spectral matrices for community detection, revealing which matrices are most effective for heterogeneous networks.

Findings

Normalized Laplacian and correlation matrices outperform others.

Node degree heterogeneity significantly impacts spectral method effectiveness.

Modularity matrix performs similarly to adjacency matrix, questioning its benefits.

Abstract

Spectral analysis has been successfully applied at the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlation matrix and several other variants of these matrices. However, the comparison between these spectral methods is less reported. More importantly, it is still unclear which matrix is more appropriate for the detection of community structure. This paper answers the question through evaluating the effectiveness of these five matrices against the benchmark networks with heterogeneous distributions of node degree and community size. Test results demonstrate that the normalized Laplacian matrix and the correlation matrix significantly outperform the other three matrices at identifying the community structure of networks. This indicates that it is crucial to take into account the heterogeneous distribution of node degree when using spectral analysis for the detection of community structure. In addition, to our surprise, the modularity matrix exhibits very similar performance to the adjacency matrix, which indicates that the modularity matrix does not gain desired benefits from using the configuration model as reference network with the consideration of the node degree heterogeneity.