{
  "abstract": "Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted simple graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances visualize how mass is shifted to transform one network into another. Beyond reviewing existing transport-based approaches, we establish new spectral lower and upper bounds for the Bures-Wasserstein distance and characterize the tightness of the lower bound under eigenbasis perturbations. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world temporal network.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27500",
  "author_total": 2,
  "authors": [
    {
      "name": "James Hyun"
    },
    {
      "name": "François G. Meyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhf3833ws3y9n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27500",
  "fulltext_url": null,
  "id": "dhf3833ws3y9n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27500",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.SI"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7204759694",
  "pdf_url": "https://arxiv.org/pdf/2608.27500",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhf3833ws3y9n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2608.27500",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27500"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications",
  "title_text": "Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/dhf3833ws3y9n",
  "venue": "arXiv",
  "versions": []
}