  Detecting communities on graphs has received significant interest in recent
literature. Current state-of-the-art community embedding approach called
\textit{ComE} tackles this problem by coupling graph embedding with community
detection. Considering the success of hyperbolic representations of
graph-structured data in last years, an ongoing challenge is to set up a
hyperbolic approach for the community detection problem. The present paper
meets this challenge by introducing a Riemannian equivalent of \textit{ComE}.
Our proposed approach combines hyperbolic embeddings with Riemannian K-means or
Riemannian mixture models to perform community detection. We illustrate the
usefulness of this framework through several experiments on real-world social
networks and comparisons with \textit{ComE} and recent hyperbolic-based
classification approaches.
