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2022 Bootstrapping exchangeable random graphs
Alden Green, Cosma Rohilla Shalizi
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Electron. J. Statist. 16(1): 1058-1095 (2022). DOI: 10.1214/21-EJS1896

Abstract

We introduce two new bootstraps for exchangeable random graphs. One, the “empirical graphon bootstrap”, is based purely on resampling, while the other, the “histogram bootstrap”, is a model-based “sieve” bootstrap. We show that both of them accurately approximate the sampling distributions of motif densities, i.e., of the normalized counts of the number of times fixed subgraphs appear in the network. These densities characterize the distribution of (infinite) exchangeable networks. Our bootstraps therefore give a valid quantification of uncertainty in inferences about fundamental network statistics, and so of parameters identifiable from them.

Funding Statement

Our work was supported by NSF grant DMS1418124.

Acknowledgments

We are grateful to the participants in the CMU Networkshop for valuable suggestions on the content and presentation of our results; to Prof. Paul Janssen for directing us to Janssen [18]; and to Profs. Carl T. Bergstrom, Peter J. Bickel, Dean Eckles, Jennifer Neville, Art B. Owen and Alessandro Rinaldo for valuable discussions, over the years, about network bootstraps.

Citation

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Alden Green. Cosma Rohilla Shalizi. "Bootstrapping exchangeable random graphs." Electron. J. Statist. 16 (1) 1058 - 1095, 2022. https://doi.org/10.1214/21-EJS1896

Information

Received: 1 August 2020; Published: 2022
First available in Project Euclid: 3 February 2022

Digital Object Identifier: 10.1214/21-EJS1896

Subjects:
Primary: 62F40
Secondary: 62G05 , 62G09

Keywords: bootstrap , exchangeable random graph , motif density , network

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