{
  "abstract": "We study exact community recovery in the Degree-Corrected Poisson Stochastic Block Model (DC-SBM) through the maximum profile likelihood estimator. Our main contribution is identifying an explicit complexity constant $C(\\pi,S)$, which closely captures the exact recovery threshold. This constant combines a weighted Chernoff--Hellinger separation between communities with a Kullback--Leibler correction induced by the degree-normalized block volumes. We rigorously prove that $C(\\pi,S)>1$ ensures the strong consistency of the maximum profile likelihood estimator, yielding exact community recovery down to the logarithmic sparsity scale. We conjecture that $C(\\pi,S)=1$ represents the sharp information-theoretic threshold, providing an upper bound on the exact-recovery transition, and we discuss analogies with the binary SBM and binary DC-SBM cases. Additionally, we establish weak consistency when the average degree diverges, offering a unified picture across sparse and dense regimes. The proofs require new control of the profile likelihood in the presence of heterogeneous degree parameters, whose node-specific weights fundamentally alter the geometry and concentration of the recovery problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15793",
  "author_total": 1,
  "authors": [
    {
      "name": "Lucie Arts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbb9gn9t6vhhw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15793",
  "fulltext_url": null,
  "id": "bbb9gn9t6vhhw",
  "issns": [],
  "landing_url": "https://hal.science/hal-05732032v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
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      "math.ST"
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      "3109|Complex Network Analysis Techniques"
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  "openalex": "W7213326846",
  "pdf_url": "https://hal.science/hal-05732032/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbb9gn9t6vhhw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05732032",
      "source": "hal",
      "url": "https://hal.science/hal-05732032v1"
    },
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Threshold Constant for Exact Community Recovery in the Degree-Corrected Poisson Stochastic Block Model",
  "title_text": "A Threshold Constant for Exact Community Recovery in the Degree-Corrected Poisson Stochastic Block Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/bbb9gn9t6vhhw",
  "venue": "HAL",
  "versions": []
}