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.
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