Open Access
October 2018 Community detection in degree-corrected block models
Chao Gao, Zongming Ma, Anderson Y. Zhang, Harrison H. Zhou
Ann. Statist. 46(5): 2153-2185 (October 2018). DOI: 10.1214/17-AOS1615


Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.


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Chao Gao. Zongming Ma. Anderson Y. Zhang. Harrison H. Zhou. "Community detection in degree-corrected block models." Ann. Statist. 46 (5) 2153 - 2185, October 2018.


Received: 1 July 2016; Revised: 1 July 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964329
MathSciNet: MR3845014
Digital Object Identifier: 10.1214/17-AOS1615

Primary: 62H30 , 91D30
Secondary: 62C20 , 90B15

Keywords: clustering , Minimax rates , network analysis , spectral clustering , Stochastic block model

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 5 • October 2018
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