Maximal diameter theorem for directed graphs of positive Ricci curvature

2020/11/02 by Ryunosuke Ozawa, Ozawa, Ryunosuke, Yohei Sakurai +3
Mathematics · Physics and Astronomy · #05C12 #05C20 #05C81 #53C21 #53C23 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2011.00755

openalex publication_date 2020/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a previous work, the authors have introduced a Lin-Lu-Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet-Myers type. In this paper, we investigate rigidity properties for the equality case, and conclude a maximal diameter theorem of Cheng type.

Citations

• Laplacians and the Cheeger Inequality for Directed Graphs
• Ricci curvature of Markov chains on metric spaces
• Inner-Outer Curvatures, Ricci-Ollivier Curvature and Volume Growth of\n Graphs

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• Cheng maximal diameter theorem for hypergraphs
• Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature
• Graphs with nonnegative Ricci curvature and maximum degree at most 3
• The Ricci curvature on directed graphs
• Refined diameter bounds under curvature dimension conditions