Long-Scale Ollivier Ricci Curvature of Graphs

Analysis and Geometry in Metric Spaces

Cushing D.¹  Kamtue S.¹ 

[1] Department of Mathematical Sciences, Durham University, United KingdomDurham;

关键词: curvature;    graphs;    optimal transport;    05c10;    52c99;    90c08;   

DOI  :  10.1515/agms-2019-0003

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown