Ollivier-Ricci idleness functions of graphs

Bourne, D.P.; Cushing, D.; Liu, S.; Muench, F.; Peyerimhoff, N.

Abstract

We study the Ollivier--Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.

Citation

Bourne, D., Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2018). Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32(2), 1408-1424. https://doi.org/10.1137/17m1134469

• Journal Article Type: Article
• Acceptance Date: Jan 22, 2018
• Online Publication Date: Jun 19, 2018
• Publication Date: Jun 19, 2018
• Deposit Date: Jan 25, 2018
• Publicly Available Date: Jan 26, 2018
• Journal: SIAM Journal on Discrete Mathematics
• Print ISSN: 0895-4801
• Electronic ISSN: 1095-7146
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Issue: 2
• Pages: 1408-1424
• DOI: https://doi.org/10.1137/17m1134469
• Public URL: https://durham-repository.worktribe.com/output/1340111