Constructions of betweenness-uniform graphs from trees
Combinatorics
2021-05-17 v1 Discrete Mathematics
Abstract
Betweenness centrality is a measure of the importance of a vertex x inside a network based on the fraction of shortest paths passing through x. We study a blow-up construction that has been shown to produce graphs with uniform distribution of betweenness. We disprove the conjecture about this procedure's universality by showing that trees with a diameter at least three cannot be transformed into betweenness-uniform by the blow-up construction. It remains open to characterize graphs for which the blow-up construction can produce betweenness-uniform graphs.
Keywords
Cite
@article{arxiv.2105.06777,
title = {Constructions of betweenness-uniform graphs from trees},
author = {David Hartman and Aneta Pokorná},
journal= {arXiv preprint arXiv:2105.06777},
year = {2021}
}