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An improved force-directed graph layout algorithm based on aesthetic criteria

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Computing and Visualization in Science

Abstract

The force-directed graph layout algorithm is one of the most widely used algorithms for drawing graphs. It aims at improving the graphs’ readability and understanding by producing high-quality drawings. However, the traditional algorithm, while trying to find the most stable position for each vertex, fails to produce graphs that satisfy different aesthetic criteria. In this paper, we present an algorithm that concerns the number of edge crossings, angular resolution and crossing angles. These aesthetic criteria are chosen because they are closely related to human comprehension. In addition, we also introduce a refinement process by applying a curved edges drawing method to further improve the angular resolution, which can also beautify the final drawing. The experimental results have shown that our approach can produce graphs in a more aesthetically pleasing way with larger angular resolution, proper crossing angles and less edge crossings.

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References

  1. Bannister, M.J., Eppstein, D., Goodrich, M.T., Trott, L.: Force-directed graph drawing using social gravity and scaling. Graph Draw. 7704, 414–425 (2013)

    Article  MathSciNet  Google Scholar 

  2. Bar, M., Neta, M.: Humans prefer curved visual objects. Psychol. Sci. 17(8), 645–648 (2006)

    Article  Google Scholar 

  3. Baur, M., Brandes, U.: Crossing reduction in circular layouts. Proc. Workshop Graph-Theor. Conc. Comput. Sci. 3353, 332–343 (2004)

    MathSciNet  Google Scholar 

  4. Bereg, S., Rozario, T.: Angle optimization of graphs embedded in the plane. arXiv:1211.4927v2 [cs.CG] (2013)

  5. Bertault, F.: A force-directed algorithm that preserves edge-crossing propweties. Inform. Process. Lett. 74, 7–13 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brandes, U., Pich, C.: An experimental study on distance-based graph drawing. Graph Draw. 5417, 218–229 (2009)

    Article  Google Scholar 

  7. Chernobelskiy, R., Cunningham, K.I., Goodrich, M.T., Kobourov, S.G., Trott, L.: Force-directed lombardi-style graph drawing. Graph Draw. 7034, 320–331 (2012)

    MathSciNet  Google Scholar 

  8. Davidson, R., Harrel, D.: Drawing graphs nicely using simulated annealing. ACM Trans. Graphics 15(4), 301–331 (1996)

    Article  Google Scholar 

  9. Didimo, W., Liotta, G., Romeo, S.A.: Topology-driven force-directed algorithms. Graph Draw. 6502, 165–176 (2011)

    MathSciNet  Google Scholar 

  10. Eades, P.: A heuristic for graph drawing. Congressus Numerantium 42, 149–160 (1984)

    MathSciNet  Google Scholar 

  11. Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw.-Pract. Exp. 21(11), 1129–1164 (1991)

  12. Gajer, P., Goodrich, M.T., Kobourov, S.G.: A multi-dimensional approach to force-directed layouts of large graphs. Comput. Geometry: Theory Appl. 29(1), 3–18 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gansner, E.R., Hu, Y., North, S.: A maxent-stress model for graph layout. IEEE Trans. Vis. Comput. Graphics 19(6), 927–940 (2013)

  14. Gansner, E.R., Koren, Y., North, S.: Graph drawing by stress majorization. Graph Draw. pp. 239–250 (2004)

  15. Hypercube graphs. http://mathworld.wolfram.com

  16. Hadany, R., Harel, D.: A multi-scale algorithm for drawing graphs nicely. Disc. Appl. Math. 113(1), 3–21 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Harel, D., Koren, Y.: A fast multi-scale method for drawing large graphs. J. Graph Algorithms Appl. 6(3), 179–202 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hobbs, R., Lombardi, M.: Global Networks. Independent Curators Inc., New York (2003)

    Google Scholar 

  19. Hua, J., Huang, M.L., Huang, W., Wang, J., Nguyen, Q.V.: Force-directed graph visualization with pre-positioning: improving convergence time and quality of layout. In: International Conference on Information Visualization, pp. 124–129 (2012)

  20. Huang, W., Hong, S.H., Eades, P.: Effects of crossing angles. In: IEEE Pacific Visualisation Symposium, pp. 41–46 (2008)

  21. Huang, W., Hong, S.H., Eades, P., Lin, C.C.: Improving multiple aesthetics produces better graph drawings. J. Visual Lang. Comput. 24(4), 262–272 (2013)

    Article  Google Scholar 

  22. Huang, W., Huang, M., Lin, C.C.: Aesthetic of angular resolution for node-link diagrams: Validation and algorithm. In: IEEE Symposium on Visual Languages and Human-Centric Computing (2011)

  23. Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Inform. Process. Lett. 31(1), 7–15 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kosak, C., Marks, J., Shieber, S.: Automating the layout of network diagrams with specified visual organization. IEEE Trans. Syst. Man Cybern. 24(3), 440–441 (1994)

    Article  Google Scholar 

  25. Lin, C.C., Yen, H.C.: A new force-directed graph drawing method based on edge-edge repulsion. J. Vis. Lang. Comput. 23, 29–42 (2012)

    Article  Google Scholar 

  26. Purchase, H., Hamer, J., Noellenburg, M., Kobourov, S.G.: On the usability of lombardi graph drawings. Graph Draw. 7704, 451–462 (2013)

    Article  Google Scholar 

  27. Purchase, H.C.: Which aesthetic has the greatest effect on human understanding? Graph Draw. 1353, 248–261 (1997)

    Article  Google Scholar 

  28. Purchase, H.C.: Metrics for graph drawing aesthetics. J. Vis. Lang. Comput. 13, 501–516 (2002)

    Article  Google Scholar 

  29. Rome graphs. http://www.graphdrawing.org/data

  30. Source code for the Kamada–Kawai algorithm. http://harambeenet.org/guess/src/guess/com/hp/hpl/guess/layout/KamadaGraphLayout.java

  31. Tutte, W.T.: How to draw a graph. Proc. Lond. Math. 3, 743–768 (1963)

    Article  MathSciNet  Google Scholar 

  32. Ware, C., Purchase, H., Colpoys, L., Mcgrill, M.: Cognitive measurements of graph aesthetics. Inform. Vis. 1(2), 103–110 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61163059 as well as the National High Technology Research and Development Program of China under Grant 2012AA011005. The authors would like to thank the reviewers for their helpful comments and constructive suggestions.

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Correspondence to Wenqiang Dong.

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Communicated by: Gabriel Wittum.

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Dong, W., Fu, X., Xu, G. et al. An improved force-directed graph layout algorithm based on aesthetic criteria. Comput. Visual Sci. 16, 139–149 (2013). https://doi.org/10.1007/s00791-014-0228-5

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  • DOI: https://doi.org/10.1007/s00791-014-0228-5

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