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

In this article, 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.

I. Introduction

Graphs are a ubiquitous form of data, whenever objects and their relations have to be represented; lots of effort has been spent on finding good ways to visualize them. Arguably one of the most prevalent representations for graphs are node-link diagrams, which are intuitive and efficient in supporting various graph analysis tasks [3].