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The Binary Stress Model for Graph Drawing

  • Yehuda Koren
  • Ali Çivril
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

We introduce a new force-directed model for computing graph layout. The model bridges the two more popular force directed approaches – the stress and the electrical-spring models – through the binary stress cost function, which is a carefully defined energy function with low descriptive complexity allowing fast computation via a Barnes-Hut scheme. This allows us to overcome optimization pitfalls from which previous methods suffer. In addition, the binary stress model often offers a unique viewpoint to the graph, which can occasionally add useful insight to its topology. The model uniformly spreads the nodes within a circle. This helps in achieving an efficient utilization of the drawing area. Moreover, the ability to uniformly spread nodes regardless of topology, becomes particularly helpful for graphs with low connectivity, or even with multiple connected components, where there is not enough structure for defining a readable layout.

Keywords

Stress Function Large Graph Graph Drawing Uniform Spread Area Utilization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Barnes, J.E., Hut, P.: A hierarchical O(N log N) force calculation algorithm. Nature 324(4), 446–449 (1986)CrossRefGoogle Scholar
  2. 2.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, Heidelberg (1997)CrossRefzbMATHGoogle Scholar
  3. 3.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  4. 4.
    Eades, P.: A heuristic for graph drawing. Cong. Numer. 42, 149–160 (1984)MathSciNetGoogle Scholar
  5. 5.
    Freivalds, K., Dogrusoz, U., Kikusts, P.: Disconnected graph layout and the polyomino packing approach. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 378–391. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Fruchterman, T.M.G., Reingold, E.: Graph drawing by force-directed placement. Software-Practice Experience 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  7. 7.
    Gansner, E., Koren, Y., North, S.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Gansner, E., Koren, Y., North, S.: Topological fisheye views for visualizing large graphs. IEEE Trans. Vis. Comput. Graph. 11(4), 457–468 (2005)CrossRefGoogle Scholar
  9. 9.
    Hachul, S., Junger, M.: Drawing large graphs with a potential-field-based multilevel algorithm. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 285–295. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Hall, K.M.: An r-dimensional quadratic placement algorithm. Management Science 17(3), 219–229 (1970)CrossRefzbMATHGoogle Scholar
  11. 11.
    Hu, Y.F.: Efficient high quality force-directed graph drawing. The Mathematica Journal 10(1), 37–71 (2005)Google Scholar
  12. 12.
    Hu, Y.F.: A gallery of large graphs, http://www.research.att.com/~yifanhu/GALLERY/GRAPHS
  13. 13.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31(1), 7–15 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  15. 15.
    Koren, Y.: Graph drawing by subspace optimization. In: Eurographics / IEEE TCVG Symposium on Visualization, pp. 65–74 (2004)Google Scholar
  16. 16.
    Kruskal, J., Seery, J.: Designing network diagrams. In: First General Conference on Social Graphics, pp. 22–50 (1980)Google Scholar
  17. 17.
    Quigley, A., Eades, P.: FADE: Graph drawing, clustering and visual abstraction. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 197–210. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Tutte, W.T.: How to Draw a Graph. Proc. London Math. Soc. s3-13(1), 743–767 (1963)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Walshaw, C.: A multilevel algorithm for force-directed graph drawing. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 171–182. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yehuda Koren
    • 1
  • Ali Çivril
    • 2
  1. 1.AT&T Labs — ResearchUSA
  2. 2.Rensselaer Polytechnic InstituteUSA

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