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PreprintarXiv licencearXiv

On harmonic centers of graphs

  • Tomáš Madaras
  • Matúš Paralič
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Abstract

The harmonic centrality of a vertex v in a graph G = (V,E) is the sum of reciprocals of distances of vertices of G from v. The vertices of G which have the maximum (minimum) harmonic centrality form the harmonic center (or periphery, resp.) of G. We study harmonic centers of graphs and their localization in graph blocks, presenting sufficient conditions for graphs (in terms of diameter or number of edges) to have those centers contained in a single block; in addition, we show that each connected graph is the harmonic center as well as harmonic periphery of some graphs.

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Cite

BibTeXRIS
BibTeX
@misc{madaras2026harmonic,
  title = {{On harmonic centers of graphs}},
  author = {Tomáš Madaras and Matúš Paralič},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31295},
  eprint = {2609.31295},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31295},
}
RIS
TY  - UNPB
TI  - On harmonic centers of graphs
AU  - Tomáš Madaras
AU  - Matúš Paralič
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31295
UR  - https://arxiv.org/abs/2609.31295
AB  - The harmonic centrality of a vertex v in a graph G = (V,E) is the sum of reciprocals of distances of vertices of G from v. The vertices of G which have the maximum (minimum) harmonic centrality form the harmonic center (or periphery, resp.) of G. We study harmonic centers of graphs and their localization in graph blocks, presenting sufficient conditions for graphs (in terms of diameter or number of edges) to have those centers contained in a single block; in addition, we show that each connected graph is the harmonic center as well as harmonic periphery of some graphs.
ER  -