Title: Bootstrapping Exchangeable Random Graphs,
Abstract: We introduce two new bootstraps for exchangeable random graphs. One, the
"empirical graphon", is based purely on resampling, while the other, the
"histogram stochastic block model", 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, for the
first time, a valid quantification of uncertainty in inferences about
fundamental network statistics, and so of parameters identifiable from them.