Coarse Ricci curvature of hypergraphs and its generalization
Metric Geometry
2026-01-21 v5
Abstract
In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also show a lower bound of nonzero eigenvalues of Laplacian, gradient estimate of heat flow, and diameter bound of Bonnet-Myers type for our curvature notion. This research leads to understanding how nonlinearity of Laplacian causes complexity of curvatures.
Keywords
Cite
@article{arxiv.2102.00698,
title = {Coarse Ricci curvature of hypergraphs and its generalization},
author = {MasaHiro Ikeda and Yu Kitabeppu and Yuuki Takai and Takato Uehara},
journal= {arXiv preprint arXiv:2102.00698},
year = {2026}
}
Comments
version accepted in Osaka Journal of Mathematics