  Network data are increasingly collected along with other variables of
interest. Our motivation is drawn from neurophysiology studies measuring brain
connectivity networks for a sample of individuals along with their membership
to a low or high creative reasoning group. It is of paramount importance to
develop statistical methods for testing of global and local changes in the
structural interconnections among brain regions across groups. We develop a
general Bayesian procedure for inference and testing of group differences in
the network structure, which relies on a nonparametric representation for the
conditional probability mass function associated with a network-valued random
variable. By leveraging a mixture of low-rank factorizations, we allow simple
global and local hypothesis testing adjusting for multiplicity. An efficient
Gibbs sampler is defined for posterior computation. We provide theoretical
results on the flexibility of the model and assess testing performance in
simulations. The approach is applied to provide novel insights on the
relationships between human brain networks and creativity.
