{
  "abstract": "DomiRank is a node-importance algorithm for unweighted networks, defined by a dynamical model governed by a competition-strength parameter, a dominance threshold, and a decay rate. We establish three structural results. First, on symmetry. Automorphism-related vertices share the same DomiRank value, and a graph whose values are pairwise distinct must be asymmetric. The orbit count bounds the number of distinct values, and regular and vertex-transitive graphs admit closed forms. Second, on entropy. The maximum of the DomiRank entropy over connected graphs, log_2 N, is attained if and only if the graph is regular. The initial entropy derivative is the degree-log-degree edge covariance, making the decrease rigorous near vanishing competition for structurally disassortative graphs, and an assortative counterexample shows it does not extend to all graphs; a sufficient-condition theorem and a refined conjecture cover the rest. Third, on spectrum. The normalized distribution is sigma-invariant if and only if the degree vector is an adjacency-matrix eigenvector. The parameter sigma interpolates continuously between degree and smallest-eigenvector centrality within the resolvent (Bonacich-type) family, its sensitivity being a second-order suppression operator on the degree vector. Graph transformations are also characterized, including the m-product. Experiments on four real networks and synthetic families up to 10^4 vertices confirm the interpolation and exhibit monotone entropy decrease, continuous ranking interpolation, decaying positive fraction and ranking reversals; where the positive fraction has decayed far from one, the limit describes the solution vector rather than the induced ranking. DomiRank is thus a tunable complement to principal-eigenvector centrality. A companion study quantifies how much of its task-level edge over a degree baseline survives degree correction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00107",
  "author_total": 2,
  "authors": [
    {
      "name": "Yingying Zhang"
    },
    {
      "name": "Chengye Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fytkygd77ja3n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00107",
  "fulltext_url": null,
  "id": "fytkygd77ja3n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00107",
  "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",
      "cs.SI"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7215984026",
  "pdf_url": "https://arxiv.org/pdf/2610.00107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fytkygd77ja3n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.00107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Structural Properties of DomiRank Centrality: Symmetry Axioms, an Entropy Bound, and Spectral Interpolation",
  "title_text": "Structural Properties of DomiRank Centrality: Symmetry Axioms, an Entropy Bound, and Spectral Interpolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/fytkygd77ja3n",
  "venue": "arXiv",
  "versions": []
}