Detecting Overlapping Communities in Networks Using Spectral Methods

TL;DR

This paper introduces a spectral algorithm based on K-medians for detecting overlapping communities in networks, demonstrating high accuracy on simulated and real social networks.

Contribution

It proposes a flexible generative model for overlapping communities and an efficient spectral method that handles overlaps better than traditional clustering techniques.

Findings

Algorithm is asymptotically consistent under certain conditions.

Performs well on both simulated and real social networks.

Outperforms benchmark methods in overlapping community detection.

Abstract

Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the K-medians algorithm rather than the usual K-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection.