  Networks with node covariates offer two advantages to community detection
methods, namely, (i) exploit covariates to improve the quality of communities,
and more importantly, (ii) explain the discovered communities by identifying
the relative importance of different covariates in them. Recent methods have
almost exclusively focused on the first point above. However, the quantitative
improvements offered by them are often due to complex black-box models like
deep neural networks at the expense of explainability. Approaches that focus on
the second point are either domain-specific or have poor performance in
practice. This paper proposes explainable, domain-independent statistical
models for networks with node covariates that additionally offer good
quantitative performance. Our models combine the strengths of Stochastic Block
Models and Restricted Boltzmann Machines to provide interpretable insights
about the communities. They support both pure and mixed community memberships.
Besides providing explainability, our approach's main strength is that it does
not explicitly assume a causal direction between community memberships and node
covariates, making it applicable in diverse domains. We derive efficient
inference procedures for our models, which can, in some cases, run in linear
time in the number of nodes and edges. Experiments on several synthetic and
real-world networks demonstrate that our models achieve close to
state-of-the-art performance on community detection and link prediction tasks
while also providing explanations for the discovered communities.
