A measure-theoretic representation of graphs

Raffaella Mulas; Giulio Zucal

doi:10.1007/s10998-023-00536-3

A measure-theoretic representation of graphs

Raffaella Mulas, Giulio Zucal^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

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	https://doi.org/10.1007/s10998-023-00536-3
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).

Keywords

Action convergence
Graph limits
Graphops
Network distances

Access to Document

10.1007/s10998-023-00536-3

Persistent URL (handle)

Copy link address

Cite this

@article{aa2058aa45a54f3ab3bedabc859b400b,

title = "A measure-theoretic representation of graphs",

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.",

keywords = "Action convergence, Graph limits, Graphops, Network distances",

author = "Raffaella Mulas and Giulio Zucal",

note = "Funding Information: Open Access funding enabled and organized by Projekt DEAL. Raffaella Mulas was supported by the Max Planck Society{\textquoteright}s Minerva Grant. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2024",

month = mar,

doi = "10.1007/s10998-023-00536-3",

language = "English",

volume = "88",

pages = "8--24",

journal = "Periodica Mathematica Hungarica",

issn = "0031-5303",

publisher = "Akad{\'e}miai Kiad{\'o}",

number = "1",

}

TY - JOUR

T1 - A measure-theoretic representation of graphs

AU - Mulas, Raffaella

AU - Zucal, Giulio

N1 - 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).

PY - 2024/3

Y1 - 2024/3

N2 - 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.

AB - 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.

KW - Action convergence

KW - Graph limits

KW - Graphops

KW - Network distances

UR - http://www.scopus.com/inward/record.url?scp=85168343911&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85168343911&partnerID=8YFLogxK

U2 - 10.1007/s10998-023-00536-3

DO - 10.1007/s10998-023-00536-3

M3 - Article

AN - SCOPUS:85168343911

SN - 0031-5303

VL - 88

SP - 8

EP - 24

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

IS - 1

ER -

A measure-theoretic representation of graphs

Abstract

Bibliographical note

Keywords

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this