  We generalize the stochastic block model to the important case in which edges
are annotated with weights drawn from an exponential family distribution. This
generalization introduces several technical difficulties for model estimation,
which we solve using a Bayesian approach. We introduce a variational algorithm
that efficiently approximates the model's posterior distribution for dense
graphs. In specific numerical experiments on edge-weighted networks, this
weighted stochastic block model outperforms the common approach of first
applying a single threshold to all weights and then applying the classic
stochastic block model, which can obscure latent block structure in networks.
This model will enable the recovery of latent structure in a broader range of
network data than was previously possible.
