A graphon counter example

TL;DR

This paper presents a specific graphon example demonstrating that not all graphons can be transformed into an equivalent form with a non-decreasing degree function, highlighting limitations in graphon representations.

Contribution

The paper provides a counterexample showing the impossibility of representing certain graphons with increasing degree functions, advancing understanding of graphon equivalence classes.

Findings

Existence of a graphon with no equivalent increasing degree function

Counterexample clarifies limitations in graphon transformations

Highlights complexity in graphon classification

Abstract

We give an example of a graphon such that there is no equivalent graphon with a degree function that is (weakly) increasing.