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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Acknowledgments
David Hartman and Aneta Pokorná were partially supported by ERC Synergy grant DYNASNET grant agreement no. 810115.
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Hartman, D., Pokorná, A. (2021). Constructions of Betweenness-Uniform Graphs from Trees. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_117
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DOI: https://doi.org/10.1007/978-3-030-83823-2_117
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