A spectral method for community detection in moderately-sparse degree-corrected stochastic block models

TL;DR

This paper introduces a spectral clustering algorithm for community detection in degree-corrected stochastic block models that works reliably in sparse regimes with heterogeneous degrees, without requiring prior parameter knowledge.

Contribution

The paper presents a parameter-free spectral clustering method that consistently detects communities in moderately sparse degree-corrected stochastic block models.

Findings

Algorithm recovers community membership for almost all nodes.

Works in regimes where minimum degree is logarithmic in network size.

Effective even with highly heterogeneous degree distributions.

Abstract

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the block-membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log$(n)$ or higher. Recovery succeeds even for very heterogeneous degree-distributions. The used algorithm does not rely on parameters as input. In particular, it does not need to know the number of communities.