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

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.

13 pages, 9 figures

References in corpus (18)

• Modularity and community structure in networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Finding community structure in networks using the eigenvectors of matrices
• Benchmark graphs for testing community detection algorithms
• Resolution limit in community detection
• Comparing community structure identification
• An information-theoretic framework for resolving community structure in complex networks
• Detect overlapping and hierarchical community structure in networks
• Analysis of the structure of complex networks at different resolution levels
• Phase transition in the detection of modules in sparse networks
• A Bayesian Approach to Network Modularity
• Community Detection as an Inference Problem
• Evaluating Local Community Methods in Networks
• Quantifying and identifying the overlapping community structure in networks
• (Un)detectable cluster structure in sparse networks
• Covariance, correlation matrix and the multi-scale community structure of networks
• Triangular clustering in document networks
• Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies