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THE RICCI CURVATURE ON DIRECTED GRAPHS

Yamada, Taiki

  • Received : 2018.02.08
  • Accepted : 2018.04.10
  • Published : 2019.01.01

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.

Keywords

graph theory;discrete differential geometry