Characterizing Edge Betweenness-Uniform graphs

Authors

Jana Coroničová Hurajová, University of Economics, TajovskéhoFollow
Tomas Madaras, P.J. Šafárik University in KošiceFollow
Darren A. Narayan, Rochester Institute of TechnologyFollow

Abstract

The betweenness centrality of an edge e is, summed over all u,v ∈ V(G), the ratio of the number of shortest u,v-paths in G containing e to the number of shortest u,v-paths in G. Graphs whose vertices all have the same edge betweenness centrality are called edge betweeness-uniform. It was recently shown by Madaras, Hurajová, Newman, Miranda, Fl´orez , and Narayan that of the over 11.7 million graphs with ten vertices or fewer, only four graphs are edge betweenness-uniform but not edge-transitive. In this paper we present new results involving properties of betweenness-uniform graphs.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Coroničová Hurajová, Jana; Madaras, Tomas; and Narayan, Darren A. (2022) "Characterizing Edge Betweenness-Uniform graphs," Theory and Applications of Graphs: Vol. 9: Iss. 1, Article 5.
DOI: 10.20429/tag.2022.090105
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/5