{
  "abstract": "We obtain tight bounds on the modularity of PPM graphs in the case of equally sized parts. Moreover, we provide a general method that can help in obtaining bounds for various other models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Comput Manag Sci 20, 34 (2023)",
  "arxiv": "2609.07896",
  "author_total": 1,
  "authors": [
    {
      "name": "M. Koshelev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2vscqc1arjfk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07896",
  "fulltext_url": null,
  "id": "b2vscqc1arjfk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07896",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.07896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2vscqc1arjfk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Modularity in planted partition model",
  "title_text": "Modularity in planted partition model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/b2vscqc1arjfk",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s10287-023-00466-y",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}