Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality

Matjaž Kovše

Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality

Combinatorics 2016-05-11 v2

Authors: Matjaž Kovše

Abstract

A formula based on a vertex contributions of the Steiner $k$ -Wiener index is induced by a newly introduced $k$ -Steiner betweenness centrality, which measures the number of $k$ -Steiner trees that include a particular vertex as a non-terminal vertex. This generalizes \v{S}krekovski and Gutman's Vertex version of the Wiener Theorem and a result of Gago on the average betweenness centrality and the average distance in general graphs.

Keywords

Steiner Wiener index Steiner betweenness centrality vertex decomposition k-Steiner trees graph theory Wiener theorem

Cite

@article{arxiv.1605.00260,
  title  = {Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality},
  author = {Matjaž Kovše},
  journal= {arXiv preprint arXiv:1605.00260},
  year   = {2016}
}

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11 pages

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