The Ricci curvature on directed graphs
Taiki Yamada
TL;DR
This paper explores Ricci curvature in directed graphs, establishing properties, conditions for Ricci-flatness, and calculating curvature for graph products, expanding understanding of geometric properties in directed network structures.
Contribution
It introduces new properties and conditions for Ricci curvature in directed graphs and computes curvature for their Cartesian products, extending existing geometric graph theory.
Findings
Conditions for Ricci-flat directed regular graphs
Ricci curvature properties of directed graphs
Curvature calculations for Cartesian graph products
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.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Ophthalmology and Eye Disorders · Geometric Analysis and Curvature Flows