Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 47 min ago
PreprintarXiv licencearXiv

Betweenness centers of graphs

  • Tomáš Madaras
  • Matúš Paralič
Open at sourcePDFDOICite

Abstract

The betweenness centrality of a vertex v in a graph G = (V,E) is the sum of the relative numbers of shortest paths of G that pass through v. The vertices of G which have the maximum (resp. minimum) betweenness induce the betweenness center (resp. betweenness periphery) of G. We study betweenness of graphs and their localization in graph blocks, presenting sufficient conditions for graphs (in terms of diameter or block sizes) to have those centers contained in a single block. Further, we show that each graph occurs as the subgraph induced by the betweenness center of some graph (as well as the subgraph induced by the betweenness periphery). For trees, we show, by an alternative proof, that their betweenness center is always contained in a path; in addition, we enumerate trees of order at most 20 according to the order of their betweenness centers.

Related

  1. On harmonic centers of graphs
    Tomáš Madaras, Matúš Paralič
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. From Transition-State Geometry to Gap Times: What Lagrangian Betweenness Measures in Chemical Reaction Dynamics
    Stephen Wiggins
    arXivPreprintCC BY 4.0Full textPhysical chemistryDynamical systemsarXiv
  3. Transversality at Virtual Centers
    Tao Chen, Yunping Jiang, Linda Keen
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  4. Cyclicity of centers on center manifolds in a 3D chaotic system with a four-wing attractor
    Vitor Gusson, Claudio Pessoa
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. A colorful Steinitz theorem with different centers
    G. Ivanov
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{madaras2026betweenness,
  title = {{Betweenness centers of graphs}},
  author = {Tomáš Madaras and Matúš Paralič},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09342},
  eprint = {2609.09342},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09342},
}
RIS
TY  - UNPB
TI  - Betweenness centers of graphs
AU  - Tomáš Madaras
AU  - Matúš Paralič
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09342
UR  - https://arxiv.org/abs/2609.09342
AB  - The betweenness centrality of a vertex v in a graph G = (V,E) is the sum of the relative numbers of shortest paths of G that pass through v. The vertices of G which have the maximum (resp. minimum) betweenness induce the betweenness center (resp. betweenness periphery) of G. We study betweenness of graphs and their localization in graph blocks, presenting sufficient conditions for graphs (in terms of diameter or block sizes) to have those centers contained in a single block. Further, we show that each graph occurs as the subgraph induced by the betweenness center of some graph (as well as the subgraph induced by the betweenness periphery). For trees, we show, by an alternative proof, that their betweenness center is always contained in a path; in addition, we enumerate trees of order at most 20 according to the order of their betweenness centers.
ER  -