# Persistent Homology Guided Force-Directed Graph Layouts

arXiv: https://arxiv.org/abs/1712.05548 · HTML: https://mlsanity.com/paper/1712.05548/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2017.

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

- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [Knowledge Graphs in Practice: Characterizing their Users, Challenges, and Visualization Opportunities](https://mlsanity.com/paper/2304.01311/) (2023)
- [A Multi-scale Graph Signature for Persistence Diagrams based on Return Probabilities of Random Walks](https://mlsanity.com/paper/2209.14264/) (2022)

## Abstract (arXiv)

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets.