Volume and diameter of a graph and Ollivier’s Ricci curvature

We obtain upper bounds of diameter and volume for finite graphs by Ollivier’s Ricci curvature.

► We obtain a volume growth of graph with a lower bound of Ricci curvature. ► We obtain an upper bound of diameter of graph with an integration of Ricci curvature. ► We obtain an upper bound of diameter with Ricci curvature and an invariant measure.