{
  "abstract": "The Ramsey community number $r_κ$ is the smallest network size at which a graph is better described by a partition into communities than by no partition, under a prescribed detection rule. On a scale-free graph this question is confounded: a block model can split the network merely to absorb its degree distribution. I compute $r_κ$ analytically for the deterministic pseudofractal scale-free web of Dorogovtsev, Goltsev, and Mendes, separating genuine community structure from degree heterogeneity with two closed-form detection rules. Under a plain Bernoulli stochastic block model, the web's natural recursive bipartition is unpreferred while small and breaks at $r_κ=1095$ nodes, with a log-evidence growing as $(\\ln 3-\\tfrac{2}{3}\\ln 2)n$. Under a degree-corrected model tested against the configuration-model null, the same partition survives, breaking far earlier at $r_κ=42$, with a log-evidence growing as $(2\\ln 3-\\tfrac{4}{3}\\ln 2)n$ -- exactly twice the plain slope, and independent of the prior. Degree correction reverses the ordering of the candidate cuts, demoting the hub-leaf split and elevating the recursive one. Because the web is self-similar, the best description is not two communities but a nested hierarchy: the degree-corrected evidence keeps rising as the partition is refined, and is maximised at of order $\\sqrt{n}$ communities of $\\sim\\sqrt{n}$ nodes. A purely local recursive rule thus builds true hierarchical community structure, over and above the scale-free degree sequence it also produces, in an exactly solvable setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Complex Networks 14, cnag040 (2026)",
  "arxiv": "2607.03010",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexei Vazquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ap4r8nnhm43b4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03010",
  "fulltext_url": null,
  "id": "ap4r8nnhm43b4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03010",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.03010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ap4r8nnhm43b4.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:14Z",
      "native_id": "2607.03010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Community structure of the pseudofractal web",
  "title_text": "Community structure of the pseudofractal web",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/ap4r8nnhm43b4",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1093/comnet/cnag040",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}