August 2023 Matching recovery threshold for correlated random graphs
Jian Ding, Hang Du
Author Affiliations +
Ann. Statist. 51(4): 1718-1743 (August 2023). DOI: 10.1214/23-AOS2305

Abstract

For two correlated graphs which are independently sub-sampled from a common Erdős–Rényi graph G(n,p), we wish to recover their latent vertex matching from the observation of these two graphs without labels. When p=nα+o(1) for α(0,1], we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.

Funding Statement

J. Ding was partially supported by NSFC Key Program Project No. 12231002. H. Du was supported in part by the elite undergraduate training program of School of Mathematical Sciences at Peking University.

Acknowledgments

We warmly thank Nicholas Wormald, Yihong Wu and Jiaming Xu for stimulating discussions. We thank anonymous reviewers for their careful reading and helpful comments.

Citation

Download Citation

Jian Ding. Hang Du. "Matching recovery threshold for correlated random graphs." Ann. Statist. 51 (4) 1718 - 1743, August 2023. https://doi.org/10.1214/23-AOS2305

Information

Received: 1 June 2022; Revised: 1 June 2023; Published: August 2023
First available in Project Euclid: 19 October 2023

Digital Object Identifier: 10.1214/23-AOS2305

Subjects:
Primary: 05C80
Secondary: 68Q87

Keywords: Correlated Erdős–Rényi random graph , information threshold , matching recovery

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.51 • No. 4 • August 2023
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