Long scale Ollivier-Ricci curvature of graphs (1801.10131v1)

Published 30 Jan 2018 in math.CO

Abstract: We study the long scale Ollivier-Ricci curvature of graphs as a function of the chosen idleness. As in the previous work on the short scale, we show that this idleness function is concave and piecewise linear with at most $3$ linear parts. We provide bounds on the length of the first and last linear pieces. We also study the long scale curvature inside the Cartesian product of two regular graphs.

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