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.
| Original language | English |
|---|---|
| Pages (from-to) | 8-24 |
| Number of pages | 17 |
| Journal | Periodica Mathematica Hungarica |
| Volume | 88 |
| Issue number | 1 |
| Early online date | 21 Aug 2023 |
| DOIs | |
| Publication status | Published - Mar 2024 |
Bibliographical note
Funding Information:Open Access funding enabled and organized by Projekt DEAL. Raffaella Mulas was supported by the Max Planck Society’s Minerva Grant.
Publisher Copyright:
© 2023, The Author(s).
Funding
Open Access funding enabled and organized by Projekt DEAL. Raffaella Mulas was supported by the Max Planck Society’s Minerva Grant.
Keywords
- Action convergence
- Graph limits
- Graphops
- Network distances