The Ricci curvature on directed graphs

2016/02/25 by Taiki Yamada, Yamada, Taiki
Mathematics · Medicine · Physics and Astronomy · #05C12 #Advanced Differential Geometry Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.1602.07779

openalex publication_date 2016/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

Related

• Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
• Ricci-flat graphs with maximum degree at most 4
• Ollivier Ricci Curvature of Directed Hypergraphs
• Lin-Lu-Yau Ricci curvature on hypergraphs
• Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs