Coarse Ricci curvature of hypergraphs and its generalization

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.

version accepted in Osaka Journal of Mathematics

References in corpus (6)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
• Diffusion Operator and Spectral Analysis for Directed Hypergraph Laplacian
• Polynomial-Time Algorithms for Submodular Laplacian Systems
• A new transport distance and its associated Ricci curvature of hypergraphs

Cited by in corpus (3)

• A new transport distance and its associated Ricci curvature of hypergraphs
• Cheng maximal diameter theorem for hypergraphs
• Nonlinear Evolution Equation Associated with Hypergraph Laplacian