We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various assumptions on the link function. In the simplest case where the link function is proportional to an indicator function, the bound matches an information lower bound that we derive.
"On the estimation of latent distances using graph distances." Electron. J. Statist. 15 (1) 722 - 747, 2021. https://doi.org/10.1214/21-EJS1801