  Detecting communities in networks is important in various domains of
applications. While a variety of methods exists to perform this task, recent
efforts propose Optimal Transport (OT) principles combined with the geometric
notion of Ollivier-Ricci curvature to classify nodes into groups by rigorously
comparing the information encoded into nodes' neighborhoods. We present an
OT-based approach that exploits recent advances in OT theory to allow tuning
for traffic penalization, which enforces different transportation schemes. As a
result, our model can flexibly capture different scenarios and thus increase
performance accuracy in recovering communities, compared to standard OT-based
formulations. We test the performance of our algorithm in both synthetic and
real networks, achieving a comparable or better performance than other OT-based
methods in the former case, while finding communities more aligned with node
metadata in real data. This pushes further our understanding of geometric
approaches in their ability to capture patterns in complex networks.
