  Community detection is an important task in network analysis, in which we aim
to learn a network partition that groups together vertices with similar
community-level connectivity patterns. By finding such groups of vertices with
similar structural roles, we extract a compact representation of the network's
large-scale structure, which can facilitate its scientific interpretation and
the prediction of unknown or future interactions. Popular approaches, including
the stochastic block model, assume edges are unweighted, which limits their
utility by throwing away potentially useful information. We introduce the
`weighted stochastic block model' (WSBM), which generalizes the stochastic
block model to networks with edge weights drawn from any exponential family
distribution. This model learns from both the presence and weight of edges,
allowing it to discover structure that would otherwise be hidden when weights
are discarded or thresholded. We describe a Bayesian variational algorithm for
efficiently approximating this model's posterior distribution over latent block
structures. We then evaluate the WSBM's performance on both edge-existence and
edge-weight prediction tasks for a set of real-world weighted networks. In all
cases, the WSBM performs as well or better than the best alternatives on these
tasks.
