Calculus of Variations and Geometric Measure Theory
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D. Bourne - D. Cushing - S. Liu - F. M√ľnch - N. Peyerimhoff

Ollivier-Ricci idleness functions of graphs

created by bourne on 14 Jun 2017
modified on 27 Aug 2018


Published Paper

Inserted: 14 jun 2017
Last Updated: 27 aug 2018

Journal: SIAM Journal on Discrete Mathematics
Volume: 32
Number: 2
Pages: 1408-1424
Year: 2018


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 3 linear parts, with at most 2 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.


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