  Clustering and community detection with multiple graphs have typically
focused on aligned graphs, where there is a mapping between nodes across the
graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are
numerous application areas with multiple graphs that are only partially
aligned, or even unaligned. These graphs are often drawn from the same
population, with communities of potentially different sizes that exhibit
similar structure. In this paper, we develop a joint stochastic blockmodel
(Joint SBM) to estimate shared communities across sets of heterogeneous
non-aligned graphs. We derive an efficient spectral clustering approach to
learn the parameters of the joint SBM. We evaluate the model on both synthetic
and real-world datasets and show that the joint model is able to exploit
cross-graph information to better estimate the communities compared to learning
separate SBMs on each individual graph.
