Detecting correlation between multiple unlabeled Gaussian networks

Taha Ameen, Bruce Hajek

Abstract: This paper studies the hypothesis testing problem to determine whether $m \geq 2$ unlabeled graphs with Gaussian edge weights are correlated under a latent permutation. Previously, a sharp detection threshold for the correlation parameter $\rho$ was established by Wu, Xu and Yu for this problem when $m = 2$. Presently, their result is leveraged to derive necessary and sufficient conditions for general $m$. In doing so, an interval for $\rho$ is uncovered for which detection is impossible using $2$ graphs alone but becomes possible with $m > 2$ graphs.