2021
DOI: 10.48550/arxiv.2105.06777
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Constructions of betweenness-uniform graphs from trees

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 betweennessuniform by the blow-up construction. It remains open to characterize graphs for which the blow-up constru… Show more

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