Yong LinRenmin University, Department of Mathematics, Beijing 100872, ChinaLinyuan LuUniversity of South Carolina, Department of Mathematics, Columbia, SC 29208, USAShing-Tung YauHarvard University, Department of Mathematics, Cambridge, MA 02138, USA
We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs.