{
  "id": "2208.07246",
  "version": "v1",
  "published": "2022-08-15T15:02:21.000Z",
  "updated": "2022-08-15T15:02:21.000Z",
  "title": "A measure-theoretic representation of graphs",
  "authors": [
    "Raffaella Mulas",
    "Giulio Zucal"
  ],
  "comment": "19 pages, 3 figures, preprint; comments and suggestions welcome",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metric on the space of matrices. Moreover, we show that such pseudo-metric is a metric on the subspace of adjacency or Laplacian matrices for graphs. Hence, in particular, we obtain a metric for isomorphism classes of graphs. Additionally, we study how some properties of graphs translate in this measure representation, and we show how our analysis contributes to a simpler understanding of action convergence of graphops.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-15T15:02:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "measure-theoretic representation",
      "action convergence",
      "graph limit theory",
      "analysis contributes",
      "pseudo-metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}