Ollivier-Ricci idleness functions of graphs

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

doi:10.1137/17m1134469

Ollivier-Ricci idleness functions of graphs

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

Authors

D.P. Bourne

D. Cushing

S. Liu

F. Muench

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

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