Spectral methods for network community detection and graph partitioning

TL;DR

This paper demonstrates that spectral algorithms for community detection and graph partitioning are fundamentally equivalent under certain conditions, unifying different approaches within spectral graph theory.

Contribution

It reveals that spectral methods for modularity maximization, statistical inference, and normalized-cut partitioning are essentially identical with specific parameter choices, unifying these techniques.

Findings

Spectral algorithms for three network problems are equivalent under certain parameters.

No fundamental difference between modularity, inference-based community detection, and graph partitioning in spectral form.

Spectral methods unify different network analysis approaches.

Abstract

We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network. We show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are, in fact, identical, and hence that, at least within the spectral approximations used here, there is no difference between the modularity- and inference-based community detection methods, or between either and graph partitioning.