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


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.


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.


Download Citation

Alden Green. Cosma Rohilla Shalizi. "Bootstrapping exchangeable random graphs." Electron. J. Statist. 16 (1) 1058 - 1095, 2022.


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

MathSciNet: MR4377133
zbMATH: 1493.62147
Digital Object Identifier: 10.1214/21-EJS1896

Primary: 62F40
Secondary: 62G05 , 62G09

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

Vol.16 • No. 1 • 2022
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