A nonparametric two-sample hypothesis testing problem for random dot   product graphs
  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. 
Minh Tang and Avanti Athreya and Daniel L. Sussman and Vince Lyzinski   and Carey E. Priebe
math.ST stat.TH