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J. Korean Math. Soc. 2019; 56(1): 113-125
Online first article July 10, 2018 Printed January 1, 2019
https://doi.org/10.4134/JKMS.j180088
Copyright © The Korean Mathematical Society.
The Ricci curvature on directed graphs
Taiki Yamada
Mathematical Institute in Tohoku University
In this paper, we consider the Ricci curvature of a {\em 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
MSC numbers: Primary 05C12; Secondary 52C99
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