Volume and diameter of a graph and Ollivier's Ricci curvature

DOI10.1016/j.ejc.2012.03.029zbMath1248.05058OpenAlexW1967200178MaRDI QIDQ449208

Seong-Hun Paeng

Publication date: 12 September 2012

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2012.03.029

zbMATH Keywords

invariant measureintegral curvature

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Distance in graphs (05C12) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

Curvature and entropy of a graph ⋮ Ollivier--Ricci Idleness Functions of Graphs ⋮ Ollivier curvature of random geometric graphs converges to Ricci curvature of their Riemannian manifolds ⋮ Geometric and spectral properties of directed graphs under a lower Ricci curvature bound ⋮ Large scale Ricci curvature on graphs ⋮ Exact and asymptotic results on coarse Ricci curvature of graphs ⋮ On the mean square displacement of a random walk on a graph ⋮ Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs ⋮ The heat flow on metric random walk spaces ⋮ Inner-outer curvatures, Ollivier-Ricci curvature and volume growth of graphs ⋮ Coverings and the heat equation on graphs: Stochastic incompleteness, the Feller property, and uniform transience ⋮ Ollivier Ricci curvature for general graph Laplacians: heat equation, Laplacian comparison, non-explosion and diameter bounds ⋮ Non-negative Ollivier curvature on graphs, reverse Poincaré inequality, Buser inequality, Liouville property, Harnack inequality and eigenvalue estimates

Cites Work

• Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
• Ricci curvature of graphs
• Ricci curvature of Markov chains on metric spaces
• Relative volume comparison with integral curvature bounds
• Integral curvature bounds, distance estimates and applications
• Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Analysis and geometry on manifolds with integral Ricci curvature bounds. II

This page was built for publication: Volume and diameter of a graph and Ollivier's Ricci curvature