  We consider the stochastic block model where connection between vertices is
perturbed by some latent (and unobserved) random geometric graph. The objective
is to prove that spectral methods are robust to this type of noise, even if
they are agnostic to the presence (or not) of the random graph. We provide
explicit regimes where the second eigenvector of the adjacency matrix is highly
correlated to the true community vector (and therefore when weak/exact recovery
is possible). This is possible thanks to a detailed analysis of the spectrum of
the latent random graph, of its own interest.
