  We discuss two views on extending existing methods for complex network
modeling which we dub the communities first and the networks first view,
respectively. Inspired by the networks first view that we attribute to White,
Boorman, and Breiger (1976)[1], we formulate the multiple-networks stochastic
blockmodel (MNSBM), which seeks to separate the observed network into
subnetworks of different types and where the problem of inferring structure in
each subnetwork becomes easier. We show how this model is specified in a
generative Bayesian framework where parameters can be inferred efficiently
using Gibbs sampling. The result is an effective multiple-membership model
without the drawbacks of introducing complex definitions of "groups" and how
they interact. We demonstrate results on the recovery of planted structure in
synthetic networks and show very encouraging results on link prediction
performances using multiple-networks models on a number of real-world network
data sets.
