{
  "abstract": "Homogeneous random graphs, also known as Erd{\\H os}-Rényi graphs, are a subset of the family of dense random graphs, specified by a graphon. We analyze several goodness-of-fit tests for these models that are based on subgraph counts. To obtain the limiting null distribution of the test statistics we use a decomposition of graph functionals, which reveals a cancellation effect. Motivated by a quasirandomness result we obtain a test that is consistent against all alternatives, and we use two popular parametric subfamilies to evaluate the other tests. The theoretical results refer to the limit $n\\to \\infty$ of the size $n$ of the graph, the behavior for finite $n$ is illustrated by simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02214",
  "author_total": 1,
  "authors": [
    {
      "name": "Rudolf Grübel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0b121htvbbq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02214",
  "fulltext_url": null,
  "id": "b0b121htvbbq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02214",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7207737341",
  "pdf_url": "https://arxiv.org/pdf/2609.02214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0b121htvbbq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Tests of graph homogeneity, subgraph counts, and quasirandomness",
  "title_text": "Tests of graph homogeneity, subgraph counts, and quasirandomness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:26Z",
  "url": "https://research.draconitic.com/paper/b0b121htvbbq0",
  "venue": "arXiv",
  "versions": []
}