  Graph clustering groups entities -- the vertices of a graph -- based on their
similarity, typically using a complex distance function over a large number of
features. Successful integration of clustering approaches in automated
decision-support systems hinges on the interpretability of the resulting
clusters. This paper addresses the problem of generating interpretable
clusters, given features of interest that signify interpretability to an
end-user, by optimizing interpretability in addition to common clustering
objectives. We propose a $\beta$-interpretable clustering algorithm that
ensures that at least $\beta$ fraction of nodes in each cluster share the same
feature value. The tunable parameter $\beta$ is user-specified. We also present
a more efficient algorithm for scenarios with $\beta\!=\!1$ and analyze the
theoretical guarantees of the two algorithms. Finally, we empirically
demonstrate the benefits of our approaches in generating interpretable clusters
using four real-world datasets. The interpretability of the clusters is
complemented by generating simple explanations denoting the feature values of
the nodes in the clusters, using frequent pattern mining.
