{
  "abstract": "Most networks, from friendships to the internet, break up into communities: groups of nodes more densely connected to one another than to the rest. A basic question has remained open: how many communities should a network have, and how does that number grow with size? Simple models bracket the possibilities. In a small-world network built from dense modules -- a caveman graph of cliques -- each module is a community, so the number grows in proportion to size, as $n$. In self-similar, fractal networks it grows far more slowly, as the square root. Real networks could lie anywhere between. Here we measure the number of communities across close to a hundred real networks spanning four orders of magnitude, from a $34$-member club to millions of nodes, and within individual systems followed over decades as they grow. We find a power law with an exponent between one half and two thirds -- above the fractal value and below the linear limit. Simple models of network growth by local rules reproduce the same super-fractal exponent, a stable and measurable property of network organization. In short, network evolution herds a system's components into clusters, whose number grows as a power law of size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18962",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexei Vazquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dt249ht04jxx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18962",
  "fulltext_url": null,
  "id": "3dt249ht04jxx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18962",
  "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",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7213515328",
  "pdf_url": "https://arxiv.org/pdf/2609.18962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dt249ht04jxx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18962"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The number of communities in real networks grows as a power law of their size",
  "title_text": "The number of communities in real networks grows as a power law of their size",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/3dt249ht04jxx",
  "venue": "arXiv",
  "versions": []
}