Ricci curvature of graphs

2011/01/01 by Yong Lin, Linyuan Lu, Linyuan Lü +2 · 5 citations
Mathematics · Physics and Astronomy · #1-planar graph #Advanced Differential Geometry Research #Cartesian product #Chordal graph #Combinatorics #Curvature #Discrete mathematics #Geometric Analysis and Curvature Flows #Geometry #Graph #Graph product #Indifference graph #Mathematics #Point processes and geometric inequalities #Ricci curvature #Scalar curvature

paper · pdf · doi:10.2748/tmj/1325886283

crossref issued 2011/01/01 · crossref published 2011/01/01 · crossref published-print 2011/01/01 · openalex publication_date 2011/01/01 · crossref created 2012/01/06 · crossref deposited 2021/05/11 · openalex created_date 2025/10/10 · crossref indexed 2026/08/04 · openalex updated_date 2026/08/04

Abstract

We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• Discrete Green's Functions
• Ricci curvature and eigenvalue estimate on locally finite graphs
• Ricci curvature of Markov chains on metric spaces

Cited by

• Edgewise Envelopes Between Balanced Forman and Ollivier-Ricci Curvature
• Deciphering the generating rules and functionalities of complex networks
• Building Archimedean Space
• Vertex evaluation of multiplex graphs using Forman Curvature
• Shing-Tung Yau [wikipedia]

Related

• Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds
• Combinatorial, Bakry-Émery, Ollivier's Ricci curvature notions and their motivation from Riemannian geometry
• The Ricci curvature on directed graphs
• Exact and Asymptotic Results on Coarse Ricci Curvature of Graphs
• Ollivier Ricci Curvature of Directed Hypergraphs