Open Access
February 2016 A goodness-of-fit test for stochastic block models
Jing Lei
Ann. Statist. 44(1): 401-424 (February 2016). DOI: 10.1214/15-AOS1370


The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models with finer structures. These results naturally lead to a consistent sequential testing estimate of the number of communities.


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Jing Lei. "A goodness-of-fit test for stochastic block models." Ann. Statist. 44 (1) 401 - 424, February 2016.


Received: 1 December 2014; Revised: 1 August 2015; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1331.62283
MathSciNet: MR3449773
Digital Object Identifier: 10.1214/15-AOS1370

Primary: 62H15

Keywords: consistency , Goodness-of-fit test , network data , Stochastic block model , Tracy–Widom distribution

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • February 2016
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