Long-Scale Ollivier Ricci Curvature of Graphs

Abstract

We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts. We provide bounds on the length of the first and last linear pieces. We also study the long-scale curvature for the Cartesian product of two regular graphs.

Keywords

• curvature
• graphs
• optimal transport
• 05c10
• 52c99
• 90c08