A Quantitative Comparison of Stress-Minimization Approaches for Offline Dynamic Graph Drawing

  • Ulrik Brandes
  • Martin Mader
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)


In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have been proposed, but little is known about their relative utility. We report on a quantitative study comparing the three prototypical extensions via their adaptation for the stress-minimization framework. While some findings are more subtle, the linking approach connecting consecutive instances of the same vertex is found to be the overall method of choice.


Classical Scaling Dynamic Graph Layout Algorithm Initial Layout Network Sequence 
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  1. 1.
    Böhringer, K.F., Paulisch, F.N.: Using constraints to achieve stability in automatic graph layout algorithms. In: Proc. of the SIGCHI Conference on Human Factors in Computing Systems (CHI 1990), pp. 43–51. ACM (1990)Google Scholar
  2. 2.
    Brandes, U., Corman, S.R.: Visual unrolling of network evolution and the analysis of dynamic discourse. Information Visualization 2(1), 40–50 (2003)CrossRefGoogle Scholar
  3. 3.
    Brandes, U., Pich, C.: An Experimental Study on Distance-Based Graph Drawing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 218–229. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Brandes, U., Wagner, D.: A Bayesian Paradigm for Dynamic Graph Layout. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 236–247. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Branke, J.: Dynamic Graph Drawing. In: Kaufmann, M., Wagner, D. (eds.) Drawing Graphs. LNCS, vol. 2025, pp. 228–246. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Bridgeman, S.S., Tamassia, R.: Difference metrics for interactive orthogonal graph drawing algorithms. Journal of Graph Algorithms and Applications 4(3), 47–74 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Diehl, S., Görg, C.: Graphs, they are Changing. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 23–30. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Erten, C., Harding, P., Kobourov, S., Wampler, K., Yee, G.: Graphael: Graph Animations with Evolving Layouts. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 98–110. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Erten, C., Kobourov, S., Le, V., Navabi, A.: Simultaneous graph drawing: Layout algorithms and visualization schemes. Journal of Graph Algorithms and Applications 9(1), 165–182 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    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
  11. 11.
    Gilbert, E.N.: Random graphs. The Annals of Mathematical Statistics 30(4), 1141–1144 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Huang, M.L., Eades, P., Wang, J.: On-line animated visualization of huge graphs using a modified spring algorithm. Journal of Visual Languages and Computing 9(6), 623–645 (1998)CrossRefGoogle Scholar
  13. 13.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31, 7–15 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Michell, L., Amos, A.: Girls, pecking order and smoking. Social Science & Medicine 44(12), 1861–1869 (1997)CrossRefGoogle Scholar
  15. 15.
    Misue, K., Eades, P., Lai, W., Sugiyama, K.: Layout adjustment and the mental map. Journal on Visual Languages and Computing 6(2), 183–210 (1995)CrossRefGoogle Scholar
  16. 16.
    Moody, J., McFarland, D.A., Bender-deMoll, S.: Dynamic Network Visualization. American Journal of Sociology 110(4), 1206–1241 (2005)CrossRefGoogle Scholar
  17. 17.
    North, S.C.: Incremental Layout with DynaDag. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 409–418. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  18. 18.
    Purchase, H.C., Samra, A.: Extremes are Better: Investigating Mental Map Preservation in Dynamic Graphs. In: Stapleton, G., Howse, J., Lee, J. (eds.) Diagrams 2008. LNCS (LNAI), vol. 5223, pp. 60–73. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Robins, G., Pattison, P., Kalish, Y., Lusher, D.: An introduction to exponential random graph (p*) models for social networks. social networks 29(2), 173–191 (2007)CrossRefGoogle Scholar
  20. 20.
    Sibson, R.: Studies in the robustness of multidimensional scaling: Procrustes statistics. Journal of the Royal Statistical Society. Series B (Methodological) 40(2), 234–238 (1978)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Snijders, T.A.B.: The statistical evaluation of social network dynamics. Sociological Methodology 31, 361–395 (2001)CrossRefGoogle Scholar
  22. 22.
    Van De Bunt, G.G., Van Duijn, M.A., Snijders, T.A.: Friendship networks through time: An actor-oriented dynamic statistical network model. Computational & Mathematical Organization Theory 5, 167–192 (1999)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Martin Mader
    • 1
  1. 1.Department of Computer & Information ScienceUniversity of KonstanzGermany

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