# Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution

arXiv: https://arxiv.org/abs/2303.03964 · HTML: https://mlsanity.com/paper/2303.03964/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2023.

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

- [Graph Learning with Distributional Edge Layouts](https://mlsanity.com/paper/2402.16402/) (2024)
- [Node Embeddings via Neighbor Embeddings](https://mlsanity.com/paper/2503.23822/) (2025)
- [Lens functions for exploring UMAP Projections with Domain Knowledge](https://mlsanity.com/paper/2405.09204/) (2024)
- [TopoAlign: Topology-Aware Visual Representation Alignment](https://mlsanity.com/paper/2605.25541/) (2026)
- [ibUMAP: Coherent and Scalable Field Evaluation for UMAP Optimization](https://mlsanity.com/paper/2610.01445/) (2026)

## Abstract (arXiv)

In this paper, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.