Recovery of latent inner products from an anisotropic Gaussian random geometric graph

We study the problem of recovering latent inner products from a random geometric graph with anisotropic Gaussian latent points. More precisely, for an i.i.d. sample $x_1, \dots, x_n \sim N(0,Σ)$ where $Σ\in \mathbb{R}^{d \times d}$, an edge $(i,j)$ is present in the graph if and only if $\langle x_i