{
  "abstract": "Pure point spectral convergence is generally unavailable for sparse graph sequences, where Laplacian eigenvalues may remain unstable under graph growth. This poses challenges for analyzing spectral operators underlying many graph-based learning methods, including graph neural networks. We identify a class of sparse bipartite graph sequences for which eigenvalue-level spectral convergence can be recovered. Focusing on graphs with strong degree heterogeneity, we exploit the convergence properties of their line-graph sequences. Using a spectral correspondence between bipartite graph Laplacians and line-graph adjacency operators, we transfer convergence guarantees from dense line-graphs back to the original sparse graphs. This framework yields eigenvalue-level spectral convergence for a class of deterministic sparse graph sequences. We further analyze superlinear preferential attachment trees, establishing convergence to an infinite-dimensional limit operator. Numerical experiments empirically support our spectral convergence results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08246",
  "author_total": 2,
  "authors": [
    {
      "name": "Roxanne Holden"
    },
    {
      "name": "Luana Ruiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x6e31w9aa14n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08246",
  "fulltext_url": null,
  "id": "5x6e31w9aa14n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08246",
  "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",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x6e31w9aa14n.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral Convergence of Sparse Bipartite Graphs via the Line-Graphon",
  "title_text": "Spectral Convergence of Sparse Bipartite Graphs via the Line-Graphon",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/5x6e31w9aa14n",
  "venue": "arXiv",
  "versions": []
}