Open Access
2022 Estimating the number of communities by spectral methods
Can M. Le, Elizaveta Levina
Author Affiliations +
Electron. J. Statist. 16(1): 3315-3342 (2022). DOI: 10.1214/21-EJS1971


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.


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Can M. Le. Elizaveta Levina. "Estimating the number of communities by spectral methods." Electron. J. Statist. 16 (1) 3315 - 3342, 2022.


Received: 1 January 2021; Published: 2022
First available in Project Euclid: 17 May 2022

MathSciNet: MR4422967
zbMATH: 1493.62313
Digital Object Identifier: 10.1214/21-EJS1971

Primary: 62H12
Secondary: 62H30

Keywords: Community detection , network analysis , Stochastic block model

Vol.16 • No. 1 • 2022
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