{
  "abstract": "Hypergraphs provide a natural framework for modeling higher-order relationships, but the development of spectral techniques with provable guarantees for general non-uniform hypergraphs remains challenging. Building on Banerjee's normalized adjacency matrix and Spiro's averaging-based diffusion framework, we develop a spectral framework for non-uniform hypergraphs and establish Cheeger's inequality for their conductance. A fundamental result in the spectral theory of hypergraphs asserts that, for every non-covering hypergraph, the second-smallest eigenvalue of its normalized Laplacian is at most one. This spectral characterization yields an improved Cheeger's inequality for non-covering hypergraphs, and we show that the resulting inequality is tight on both sides using cycle and cube hypergraphs. Our framework further yields higher-order Cheeger inequalities and provides theoretical guarantees for Fiedler's spectral partitioning algorithm, all in the setting of hypergraphs. Finally and most notably, we construct a new family of optimal hypergraph expanders that is tight for the Alon--Boppana bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16286",
  "author_total": 2,
  "authors": [
    {
      "name": "Raj Kamal"
    },
    {
      "name": "Amitabha Bagchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbpw8h5xfekt2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16286",
  "fulltext_url": null,
  "id": "fbpw8h5xfekt2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16286",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7213390793",
  "pdf_url": "https://arxiv.org/pdf/2609.16286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbpw8h5xfekt2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Cheeger Inequality for Hypergraphs and Its Applications",
  "title_text": "A Cheeger Inequality for Hypergraphs and Its Applications",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fbpw8h5xfekt2",
  "venue": "arXiv",
  "versions": []
}