Multiway spectral community detection in networks

TL;DR

This paper introduces a novel spectral algorithm for directly detecting multiple communities in networks, overcoming previous limitations to only two or three communities, and demonstrates its superior performance on real-world data.

Contribution

The paper presents a new spectral algorithm that enables direct multi-community detection in networks, improving upon existing methods that were limited to few communities.

Findings

The new algorithm outperforms previous methods in accuracy.

It effectively handles unbalanced community sizes.

Applications to real networks show good agreement with expectations.

Abstract

One of the most widely used methods for community detection in networks is the maximization of the quality function known as modularity. Of the many maximization techniques that have been used in this context, some of the most conceptually attractive are the spectral methods, which are based on the eigenvectors of the modularity matrix. Spectral algorithms have, however, been limited by and large to the division of networks into only two or three communities, with divisions into more than three being achieved by repeated two-way division. Here we present a spectral algorithm that can directly divide a network into any number of communities. The algorithm makes use of a mapping from modularity maximization to a vector partitioning problem, combined with a fast heuristic for vector partitioning. We compare the performance of this spectral algorithm with previous approaches and find it to give superior results, particularly in cases where community sizes are unbalanced. We also give demonstrative applications of the algorithm to two real-world networks and find that it produces results in good agreement with expectations for the networks studied.