{
  "abstract": "The maximum likelihood degree of a Gaussian graphical model measures the algebraic complexity of its likelihood equations. This paper studies maximum likelihood degrees of Gaussian graphical models through chordal completion. When a graph becomes chordal after one missing edge is added, its maximum likelihood degree is determined by the maximal cliques and clique-tree separators containing that edge. This recovers Uhler's formula for complete bipartite graphs with one part of size two, and extends it to deleted-spine clique books, whose degree is unchanged when a page is thickened to a clique. For several fill edges, the same method gives a product formula when no clique or separator bag contains two fill edges. We also determine four classes of vertices at which clique blow-up preserves the degree. Two follow from known results, and two are established here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19669",
  "author_total": 1,
  "authors": [
    {
      "name": "Nilava Metya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60b3qhfn8n8tj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19669",
  "fulltext_url": null,
  "id": "60b3qhfn8n8tj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19669",
  "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",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7221850706",
  "pdf_url": "https://arxiv.org/pdf/2610.19669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60b3qhfn8n8tj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Maximum Likelihood Degrees via One-Edge Chordal Completion",
  "title_text": "Maximum Likelihood Degrees via One-Edge Chordal Completion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/60b3qhfn8n8tj",
  "venue": "arXiv",
  "versions": []
}