# Steady and ranging sets in graph persistence

arXiv: https://arxiv.org/abs/2009.06897 · HTML: https://mlsanity.com/paper/2009.06897/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Generalized Permutants and Graph GENEOs](https://mlsanity.com/paper/2206.14798/) (2022)
- [Graph Persistence goes Spectral](https://mlsanity.com/paper/2506.06571/) (2025)
- [Persistence-based operators in machine learning](https://mlsanity.com/paper/2212.13985/) (2022)

## Abstract (arXiv)

Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce textitsteady and textitranging sets: two standardized ways of producing persistence diagrams directly from graph-theoretical features. The two constructions are framed in the context of textitindexing-aware persistence functions. Furthermore, we introduce a sufficient condition for stability. Finally, we apply the steady- and ranging-based persistence constructions to toy examples and real-world applications.