Estimating the number of communities in networks by spectral methods

TL;DR

This paper introduces a fast spectral method for estimating the number of communities in networks, which is crucial for community detection but often unknown in practice, demonstrating high accuracy and efficiency.

Contribution

The paper proposes a novel spectral approach using the non-backtracking and Bethe Hessian matrices to estimate community numbers, outperforming existing methods in accuracy and speed.

Findings

Method performs well across various models and parameters

Guarantees consistency under multiple asymptotic regimes

More accurate and computationally efficient than existing methods

Abstract

Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a simple and very fast method for estimating the number of communities based on the spectral properties of certain graph operators, such as the non-backtracking matrix and the Bethe Hessian matrix. We show that the method performs well under several models and a wide range of parameters, and is guaranteed to be consistent under several asymptotic regimes. We compare this method to several existing methods for estimating the number of communities and show that it is both more accurate and more computationally efficient.