Long-Scale Ollivier Ricci Curvature of Graphs

Cushing, D.; Kamtue, S.

doi:10.1515/agms-2019-0003

Long-Scale Ollivier Ricci Curvature of Graphs

Cushing, D.; Kamtue, S.

Authors

D. Cushing

Supanat Kamtue supanat.kamtue@durham.ac.uk
PGR Student Doctor of Philosophy

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
Publisher	De Gruyter Open
Peer Reviewed	Peer Reviewed
Volume	7
Issue	1
Pages	22-44
DOI	https://doi.org/10.1515/agms-2019-0003

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2019 D. Cushing and S. Kamtue, published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License.