A new transport distance and its associated Ricci curvature of hypergraphs

Abstract

The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin-Lu-Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a generalization of Lin-Lu-Yau type curvature of hypergraphs. As an application, we derive a Bonnet-Myers type estimate for hypergraphs under a lower Ricci curvature bound associated with our transport distance. We remark that our transport distance is new even for graphs and worthy of further study.