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February 2021 Convex Relaxation Methods for Community Detection
Xiaodong Li, Yudong Chen, Jiaming Xu
Statist. Sci. 36(1): 2-15 (February 2021). DOI: 10.1214/19-STS715


This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees.

This survey is not intended to be a complete overview of the vast literature on this fast-growing topic. Instead, we aim to provide a big picture of the remarkable recent development in this area and to make the survey accessible to a broad audience. We hope that this expository article can serve as an introductory guide for readers who are interested in using, designing, and analyzing convex relaxation methods in network analysis.


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Xiaodong Li. Yudong Chen. Jiaming Xu. "Convex Relaxation Methods for Community Detection." Statist. Sci. 36 (1) 2 - 15, February 2021.


Published: February 2021
First available in Project Euclid: 21 December 2020

MathSciNet: MR4194200
Digital Object Identifier: 10.1214/19-STS715

Keywords: assortativity , Community detection , degree correction , robustness , semidefinite program , strong consistency , weak consistency

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.36 • No. 1 • February 2021
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