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arXiv · 2105.06777

Constructions of betweenness-uniform graphs from trees

David Hartman·Aneta Pokorná
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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.

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David Hartman, Aneta Pokorná. 2021-05-14. Constructions of betweenness-uniform graphs from trees. https://arxiv.org/abs/2105.06777

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