# Homological Scaffold via Minimal Homology Bases

arXiv: https://arxiv.org/abs/2004.11606 · HTML: https://mlsanity.com/paper/2004.11606/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

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

- [Tight basis cycle representatives for persistent homology of large data sets](https://mlsanity.com/paper/2206.02925/) (2022)
- [Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis](https://mlsanity.com/paper/2509.08350/) (2025)

## Abstract (arXiv)

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.