# The Reeb Graph Edit Distance is Universal

arXiv: https://arxiv.org/abs/1801.01866 · HTML: https://mlsanity.com/paper/1801.01866/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Rapid and Precise Topological Comparison with Merge Tree Neural Networks](https://mlsanity.com/paper/2404.05879/) (2024)
- [The Universal ℓp-Metric on Merge Trees](https://mlsanity.com/paper/2112.12165/) (2021)

## Abstract (arXiv)

We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.