Lin-Lu-Yau Ricci curvature on hypergraphs

2025/07/05 by Tian, Yulu, Zhao, Liang
#05C10 #05C65 #05C81 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.04109

Abstract

In this paper, we introduce a unified framework for defining Lin-Lu-Yau (LLY) Ricci curvature on both undirected and directed hypergraphs. By establishing upper bounds and monotonicity properties for the parameterized curvature κ_α, we justify the well-posedness and compatibility of our definitions. Furthermore, we prove a Bonnet-Myers-type theorem for hypergraphs, which highlights the potential of LLY Ricci curvature in hypergraph analysis, particularly in studying geometric and structural properties. Our results extends the foundational definitions of graph Ricci curvature by Ollivier and Lin-Lu-Yau to the hypergraph setting.

Citations

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Related

• Coarse Ricci curvature of hypergraphs and its generalization
• Ollivier Ricci Curvature of Directed Hypergraphs
• Weak Kantorovich difference and associated Ricci curvature of hypergraphs
• The Ricci curvature on directed graphs
• Integral Ricci Curvature for Graphs