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August 2021 Community detection with dependent connectivity
Yubai Yuan, Annie Qu
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Ann. Statist. 49(4): 2378-2428 (August 2021). DOI: 10.1214/20-AOS2042


In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate intra-community dependence of connectivities through the Bahadur representation. The proposed method does not require specifying the likelihood function, which could be intractable for correlated binary connectivities. In addition, the proposed method allows for heterogeneity among edges between different communities. In theory, we show that incorporating correlation information can achieve a faster convergence rate compared to the independent SBM, and the proposed algorithm has a lower estimation bias and accelerated convergence compared to the variational EM. Our simulation studies show that the proposed algorithm outperforms the existing multinetwork community detection methods assuming conditional independence among edges. We also demonstrate the application of the proposed method to agricultural product trading networks from different countries and to brain fMRI imaging networks.

Funding Statement

The work is supported by NSF grants DMS 1952406 and DMS 1821198.


The authors would like to thank two anonymous referees, the Associate Editor and the Editor for their constructive comments and help feedback that improved the quality of this paper.


Download Citation

Yubai Yuan. Annie Qu. "Community detection with dependent connectivity." Ann. Statist. 49 (4) 2378 - 2428, August 2021.


Received: 1 May 2020; Revised: 1 October 2020; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/20-AOS2042

Primary: 62R07
Secondary: 62E17

Keywords: Bahadur representation , high-order approximation , multiple networks , Stochastic block model , variational EM

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 4 • August 2021
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