  Learning community structures in graphs has broad applications across
scientific domains. While graph neural networks (GNNs) have been successful in
encoding graph structures, existing GNN-based methods for community detection
are limited by requiring knowledge of the number of communities in advance, in
addition to lacking a proper probabilistic formulation to handle uncertainty.
We propose a simple framework for amortized community detection, which
addresses both of these issues by combining the expressive power of GNNs with
recent methods for amortized clustering. Our models consist of a graph
representation backbone that extracts structural information and an amortized
clustering network that naturally handles variable numbers of clusters. Both
components combine into well-defined models of the posterior distribution of
graph communities and are jointly optimized given labeled graphs. At inference
time, the models yield parallel samples from the posterior of community labels,
quantifying uncertainty in a principled way. We evaluate several models from
our framework on synthetic and real datasets, and demonstrate improved
performance compared to previous methods. As a separate contribution, we extend
recent amortized probabilistic clustering architectures by adding attention
modules, which yield further improvements on community detection tasks.
