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Ollivier-Ricci idleness functions of graphs.

Bourne, D.P. and Cushing, D. and Liu, S. and Muench, F. and Peyerimhoff, N. (2018) 'Ollivier-Ricci idleness functions of graphs.', SIAM journal on discrete mathematics., 32 (2). pp. 1408-1424.


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.

Item Type:Article
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Publisher statement:© 2018, Society for Industrial and Applied Mathematics
Date accepted:22 January 2018
Date deposited:26 January 2018
Date of first online publication:19 June 2018
Date first made open access:No date available

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