  Random geometric graphs are a popular choice for a latent points generative
model for networks. Their definition is based on a sample of $n$ points
$X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which
represents the latent positions of nodes of the network. The connection
probabilities between the nodes are determined by an unknown function (referred
to as the "link" function) evaluated at the distance between the latent points.
We introduce a spectral estimator of the pairwise distance between latent
points and we prove that its rate of convergence is the same as the
nonparametric estimation of a function on $\mathbb{S}^{d-1}$, up to a
logarithmic factor. In addition, we provide an efficient spectral algorithm to
compute this estimator without any knowledge on the nonparametric link
function. As a byproduct, our method can also consistently estimate the
dimension $d$ of the latent space.
