  In bipartite networks, community structures are restricted to being
disassortative, in that nodes of one type are grouped according to common
patterns of connection with nodes of the other type. This makes the stochastic
block model (SBM), a highly flexible generative model for networks with block
structure, an intuitive choice for bipartite community detection. However,
typical formulations of the SBM do not make use of the special structure of
bipartite networks. Here we introduce a Bayesian nonparametric formulation of
the SBM and a corresponding algorithm to efficiently find communities in
bipartite networks which parsimoniously chooses the number of communities. The
biSBM improves community detection results over general SBMs when data are
noisy, improves the model resolution limit by a factor of $\sqrt{2}$, and
expands our understanding of the complicated optimization landscape associated
with community detection tasks. A direct comparison of certain terms of the
prior distributions in the biSBM and a related high-resolution hierarchical SBM
also reveals a counterintuitive regime of community detection problems,
populated by smaller and sparser networks, where nonhierarchical models
outperform their more flexible counterpart.
