{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31295",
  "author_total": 2,
  "authors": [
    {
      "name": "Tomáš Madaras"
    },
    {
      "name": "Matúš Paralič"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43nax8xcry335.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31295",
  "fulltext_url": null,
  "id": "43nax8xcry335",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31295",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214613228",
  "pdf_url": "https://arxiv.org/pdf/2609.31295",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43nax8xcry335.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31295",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31295"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On harmonic centers of graphs",
  "title_text": "On harmonic centers of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/43nax8xcry335",
  "venue": "arXiv",
  "versions": []
}