A nonparametric two-sample hypothesis testing problem for random dot product graphs

Abstract

We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or projection. We propose a test statistic that is a kernel-based function of the adjacency spectral embedding for each graph. We obtain a limiting distribution for our test statistic under the null and we show that our test procedure is consistent across a broad range of alternatives.

24 pages, 1 figures

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• Modularity and community structure in networks
• Stochastic blockmodels and community structure in networks
• Brownian distance covariance
• Graph limits and exchangeable random graphs

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