Annals of Statistics

Community detection in degree-corrected block models

Chao Gao, Zongming Ma, Anderson Y. Zhang, and Harrison H. Zhou

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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.

Article information

Ann. Statist., Volume 46, Number 5 (2018), 2153-2185.

Received: July 2016
Revised: July 2017
First available in Project Euclid: 17 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 91D30: Social networks
Secondary: 62C20: Minimax procedures 90B15: Network models, stochastic

Clustering Minimax rates network analysis spectral clustering stochastic block model


Gao, Chao; Ma, Zongming; Zhang, Anderson Y.; Zhou, Harrison H. Community detection in degree-corrected block models. Ann. Statist. 46 (2018), no. 5, 2153--2185. doi:10.1214/17-AOS1615.

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Supplemental materials

  • Supplement to “Community detection in degree-corrected block models.”. The supplement [11] presents additional numerical results, additional proofs of main results, properties of $J_{t}(p,q)$ and proofs of auxiliary results.