# Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs

arXiv: https://arxiv.org/abs/1804.11242 · HTML: https://mlsanity.com/paper/1804.11242/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 5 of 5)

- [Explainable Mapper: Charting LLM Embedding Spaces Using Perturbation-Based Explanation and Verification Agents](https://mlsanity.com/paper/2507.18607/) (2025)
- [AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm](https://mlsanity.com/paper/2408.06958/) (2024)
- [Positional Encoding meets Persistent Homology on Graphs](https://mlsanity.com/paper/2506.05814/) (2025)
- [Visualization Tasks for Unlabeled Graphs](https://mlsanity.com/paper/2504.14115/) (2025)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)

## Abstract (arXiv)

Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph structures, even for moderately sized data of a few hundred nodes, due to visual clutter. We propose to apply the mapper construction -- a popular tool in topological data analysis -- to graph visualization, which provides a strong theoretical basis for summarizing the data while preserving their core structures. We develop a variation of the mapper construction targeting weighted, undirected graphs, called mog, which generates homology-preserving skeletons of graphs. We further show how the adjustment of a single parameter enables multi-scale skeletonization of the input graph. We provide a software tool that enables interactive explorations of such skeletons and demonstrate the effectiveness of our method for synthetic and real-world data.