Ollivier curvature, betweenness centrality and average distance
Combinatorics
2022-10-03 v1 Differential Geometry
Abstract
We give a new upper bound for the average graph distance in terms of the average Ollivier curvature. Here, the average Ollivier curvature is weighted with the edge betweenness centrality. Moreover, we prove that equality is attained precisely for the reflective graphs which have been classified as Cartesian products of cocktail party graphs, Johnson graphs, halved cubes, Schl\"afli graphs, and Gosset graphs.
Keywords
Cite
@article{arxiv.2209.15564,
title = {Ollivier curvature, betweenness centrality and average distance},
author = {Florentin Münch},
journal= {arXiv preprint arXiv:2209.15564},
year = {2022}
}