Bootstrapping Exchangeable Random Graphs

TL;DR

This paper introduces two bootstrap methods for exchangeable random graphs, enabling accurate uncertainty quantification of motif densities and fundamental network statistics.

Contribution

The paper presents the empirical graphon bootstrap and histogram bootstrap, novel resampling techniques for exchangeable graphs, with proven accuracy in approximating motif density distributions.

Findings

Both bootstraps accurately approximate motif density sampling distributions.

The methods provide valid uncertainty quantification for network parameters.

They are applicable to inferences about exchangeable network models.

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.