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We propose a valid and consistent test for the hypothesis that two latentdistance random graphs on the same vertex set have the same generating latentpositions, up to some unidentifiable similarity transformations. Our teststatistic is based on first estimating the edge probabilities matrices bytruncating the singular value decompositions of the averaged adjacency matricesin each population and then computing a Spearman rank correlation coefficientbetween these estimates. Experimental results on simulated data indicate thatthe test procedure has power even when there is only one sample from eachpopulation, provided that the number of vertices is not too small. Applicationon a dataset of neural connectome graphs showed that we can distinguish betweenscans from different age groups while application on a dataset of epileptogenicrecordings showed that we can discriminate between seizure and non-seizureevents.

Two-sample Testing on Latent Distance Graphs With Unknown Link Functions