@article{Rengaswami2025, 
author = {Sathya Rengaswami and Theodora Bourni and Vasileios Maroulas},
title = {On the relation between graph Ricci curvature and community structure},
year = {2025},
journal = {Mathematics in Engineering},
volume = {7},
number = {2},
pages = {178-193},
keywords = {discrete curvature, Ollivier Ricci curvature, graph curvature, optimal transport, community structure, community detection},
url = {https://www.sciopen.com/article/10.3934/mine.2025008},
doi = {10.3934/mine.2025008},
abstract = {The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph.}
}