# On convergence for graphexes

## TL;DR

This paper investigates four different types of convergence for graphexes, analyzing their properties and relationships, and extends existing results on empirical graphon convergence.

## Contribution

It provides a comprehensive comparison of four convergence notions for graphexes and extends prior work on empirical graphon convergence.

## Key findings

- Analyzed properties of four convergence notions
- Established relations between different convergence types
- Extended results on empirical graphon convergence

## Abstract

We study four different notions of convergence for graphexes, recently introduced by Borgs, Chayes, Cohn and Holden, and by Veitch and Roy. We give some properties of them and some relations between them. We also extend results by Veitch and Roy on convergence of empirical graphons.