{
  "abstract": "Let $r\\geq3$ be fixed, and let $\\mathbf{G}_n$ be the set of all simple graphs with vertex set $[n]=\\{1,\\ldots,n\\}$. We consider an exponential random graph model which gives higher probability to $G \\in \\mathbf{G}_n$ than to $H \\in \\mathbf{G}_n$ if $G$ has fewer $r$-cliques than $H$. But all graphs in $\\mathbf{G}_n$ have positive probability. The degree to which graphs with fewer $r$-cliques are given higher probability is determined by a positive weight $w$. We prove that, asymptotically almost surely as $n \\to \\infty$, a random graph from $\\mathbf{G}_n$ has a vertex partition into $r-1$ parts of roughly equal size, the density of edges between the parts is close to $1/2$, and for every $\\varepsilon > 0$ the density of edges within any part is less than $\\varepsilon$. The asymptotic structural properties are independent of the weight $w$ as long as it is positive. We also extend the result to the context of several clique sizes, each one with its own weight.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30869",
  "author_total": 2,
  "authors": [
    {
      "name": "Yasmin Tousinejad"
    },
    {
      "name": "Vera Koponen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bn1ssecfzyhmd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30869",
  "fulltext_url": null,
  "id": "bn1ssecfzyhmd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30869",
  "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",
      "cs.AI"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7204944316",
  "pdf_url": "https://arxiv.org/pdf/2608.30869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bn1ssecfzyhmd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential random graph models with soft clique constraints",
  "title_text": "Exponential random graph models with soft clique constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/bn1ssecfzyhmd",
  "venue": "arXiv",
  "versions": []
}