A measuretheoretic representation of graphs
Abstract
Inspired by the notion of action convergence in graph limit theory, we introduce a measuretheoretic representation of matrices, and we use it to define a new notion of pseudometric on the space of matrices. Moreover, we show that such pseudometric 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.07246
 Bibcode:
 2022arXiv220807246M
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Probability
 EPrint:
 19 pages, 3 figures, preprint