Mathematica Journal
Volume 10, Issue 1


In This Issue
Trott's Corner
New Products
New Publications
News Bulletins
New Resources

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Back Issues
Contact Information

Efficient, High-Quality Force-Directed Graph Drawing
Yifan Hu

We propose a graph drawing algorithm that is both efficient and high quality. This algorithm combines a multilevel approach, which effectively overcomes local minimums, with the Barnes and Hut [1] octree technique, which approximates short- and long-range force efficiently. Our numerical results show that the algorithm is comparable in speed to Walshaw's [2] highly efficient multilevel graph drawing algorithm, yet gives better results on some of the difficult problems. In addition, an adaptive cooling scheme for the force-directed algorithms and a general repulsive force model are proposed. The proposed graph drawing algorithm and others are included with Mathematica 5.1 and later versions in the package DiscreteMath`GraphPlot.




*1. Introduction

*2. Definitions and Notations

*3. Force-Directed Algorithms

*4. Barnes-Hut Force Calculation

*5. The Multilevel Algorithm

*6. Numerical Results

*7. Conclusions and Future Work



Yifan Hu
Senior Developer
Wolfram Research, Inc.
100 Trade Center Drive
Champaign, IL 61820, USA

About Mathematica | Download Mathematica Player
© Wolfram Media, Inc. All rights reserved.