  We consider a blind identification problem in which we aim to recover a
statistical model of a network without knowledge of the network's edges, but
based solely on nodal observations of a certain process. More concretely, we
focus on observations that consist of single snapshots taken from multiple
trajectories of a diffusive process that evolves over the unknown network. We
model the network as generated from an independent draw from a latent
stochastic block model (SBM), and our goal is to infer both the partition of
the nodes into blocks, as well as the parameters of this SBM. We discuss some
non-identifiability issues related to this problem and present simple spectral
algorithms that provably solve the partition recovery and parameter estimation
problems with high accuracy. Our analysis relies on recent results in random
matrix theory and covariance estimation, and associated concentration
inequalities. We illustrate our results with several numerical experiments.
