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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.
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참고문헌 (11)
참고문헌 신청
J. Jost / 2014 / Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs / Discrete Comput. Geom 51(2):300~322
Y. Lin / 2011 / Ricci curvature of graphs / Tohoku Math. J 63(4):605~627
Y. Lin / 2014 / Ricci-at graphs with girth at least five / Comm. Anal. Geom 22(4):671~687
C.-C. Ni / 2015 / Ricci curvature of the Internet topology / Proceedings of the IEEE Conference on Computer Communications, INFO-COM 2015
Y. Ollivier / 2009 / Ricci curvature of Markov chains on metric spaces / J. Funct. Anal 256(3):810~864
Y. Lin / 2011 / Ricci curvature of graphs / Tohoku Math. J 63(4):605~627
Y. Lin / 2014 / Ricci-at graphs with girth at least five / Comm. Anal. Geom 22(4):671~687
C.-C. Ni / 2015 / Ricci curvature of the Internet topology / Proceedings of the IEEE Conference on Computer Communications, INFO-COM 2015
Y. Ollivier / 2009 / Ricci curvature of Markov chains on metric spaces / J. Funct. Anal 256(3):810~864
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