English

Long scale Ollivier-Ricci curvature of graphs

Combinatorics 2018-01-31 v1

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 33 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.

Keywords

Cite

@article{arxiv.1801.10131,
  title  = {Long scale Ollivier-Ricci curvature of graphs},
  author = {David Cushing and Supanat Kamtue},
  journal= {arXiv preprint arXiv:1801.10131},
  year   = {2018}
}