Two-Sample Testing for Random Graphs without Vertex Correspondence

תקציר מקורי באנגליתarXiv:2610.07503v1 Announce Type: cross Abstract: Two populations of graphs often have to be compared without any correspondence between their vertices, for instance when networks come from different communities, or when a graph generative model is evaluated against held-out graphs. We study how many graphs such an unaligned two-sample test needs, and which graph statistics can detect which differences. For an Erd\H{o}s--R\'enyi null and a planted two-block difference that leaves every expected degree unchanged, we show that $m\asymp t^{-3}$ graphs per group are necessary and sufficient when the per-graph signal-to-noise ratio is $t<1$. Signed triangle counts attain this rate, and the lower bound holds for every graph size. With aligned vertices $m\asymp t^{-1}$ graphs suffice, so misalign