Long-Scale Ollivier Ricci Curvature of Graphs

Cushing, D.; Kamtue, S.

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.

Citation

Cushing, D., & Kamtue, S. (2019). Long-Scale Ollivier Ricci Curvature of Graphs. Analysis and Geometry in Metric Spaces, 7(1), 22-44. https://doi.org/10.1515/agms-2019-0003

• Journal Article Type: Article
• Online Publication Date: May 24, 2019
• Publication Date: Mar 31, 2019
• Deposit Date: Jul 3, 2019
• Publicly Available Date: Jul 3, 2019
• Journal: Analysis and Geometry in Metric Spaces
• Electronic ISSN: 2299-3274
• Publisher: De Gruyter Open
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 1
• Pages: 22-44
• DOI: https://doi.org/10.1515/agms-2019-0003
• Public URL: https://durham-repository.worktribe.com/output/1293057