Geodesic
More on betweenness-uniform graphs
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 293-306.

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We study graphs whose vertices possess the same value of betweenness centrality (which is defined as the sum of relative numbers of shortest paths passing through a given vertex). Extending previously known results of S. Gago, J. Hurajová, T. Madaras (2013), we show that, apart of cycles, such graphs cannot contain 2-valent vertices and, moreover, are 3-connected if their diameter is 2. In addition, we prove that the betweenness uniformity is satisfied in a wide graph family of semi-symmetric graphs, which enables us to construct a variety of nontrivial cubic betweenness-uniform graphs.
DOI : 10.21136/CMJ.2018.0087-16
Classification : 05C15
Keywords: betweenness centrality; betweenness-uniform graph 
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Coroničová Hurajová, Jana; Madaras, Tomáš. More on betweenness-uniform graphs. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 293-306. doi : 10.21136/CMJ.2018.0087-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0087-16/

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