TY  - JOUR
A1  - Bourne, D. P.
A1  - Cushing, D.
A1  - Liu, S.
A1  - Münch, Florentin
A1  - Peyerimhoff, Norbert
T1  - Ollivier-Ricci idleness functions of graphs
JF  - SIAM Journal on Discrete Mathematics
N2  - 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.
KW  - Ollivier-Ricci
KW  - idleness
KW  - optimal transport
Y1  - 2018
U6  - https://doi.org/10.1137/17M1134469
SN  - 0895-4801
SN  - 1095-7146
VL  - 32
IS  - 2
SP  - 1408
EP  - 1424
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -