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.

15 pages; minor revisions, to appear in Anal. Geom. Metr. Spaces

References in corpus (2)

• Coarse Ricci curvature of hypergraphs and its generalization
• Cheng maximal diameter theorem for hypergraphs

Cited by in corpus (3)

• Coarse Ricci curvature of hypergraphs and its generalization
• Finding Influential Cores via Normalized Ricci Flows in Directed and Undirected Hypergraphs with Applications
• Weak Kantorovich difference and associated Ricci curvature of hypergraphs