  Stochastic blockmodels (SBM) and their variants, $e.g.$, mixed-membership and
overlapping stochastic blockmodels, are latent variable based generative models
for graphs. They have proven to be successful for various tasks, such as
discovering the community structure and link prediction on graph-structured
data. Recently, graph neural networks, $e.g.$, graph convolutional networks,
have also emerged as a promising approach to learn powerful representations
(embeddings) for the nodes in the graph, by exploiting graph properties such as
locality and invariance. In this work, we unify these two directions by
developing a \emph{sparse} variational autoencoder for graphs, that retains the
interpretability of SBMs, while also enjoying the excellent predictive
performance of graph neural nets. Moreover, our framework is accompanied by a
fast recognition model that enables fast inference of the node embeddings
(which are of independent interest for inference in SBM and its variants).
Although we develop this framework for a particular type of SBM, namely the
\emph{overlapping} stochastic blockmodel, the proposed framework can be adapted
readily for other types of SBMs. Experimental results on several benchmarks
demonstrate encouraging results on link prediction while learning an
interpretable latent structure that can be used for community discovery.
