Exploring Complex Drawings via Edge Stratification

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Fabrizio Montecchiani
  • Ioannis G. Tollis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

We propose an approach that allows a user to explore a layout produced by any graph drawing algorithm, in order to reduce the visual complexity and clarify its presentation. Our approach is based on stratifying the drawing into layers with desired properties; layers can be explored and combined by the user to gradually acquire details. We present stratification heuristics, a user study, and an experimental analysis that evaluates how our stratification heuristics behave on the drawings computed by a variety of popular force-directed algorithms.

References

  1. 1.
    Auber, D., Chiricota, Y., Jourdan, F., Melançon, G.: Multiscale visualization of small world networks. In: InfoVis 2003, pp. 75–81. IEEE (2003)Google Scholar
  2. 2.
    Barabasi, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Batagelj, V., Brandenburg, F., Didimo, W., Liotta, G., Palladino, P., Patrignani, M.: Visual analysis of large graphs using (X,Y)-clustering and hybrid visualizations. IEEE TVCG 17(11), 1587–1598 (2011)Google Scholar
  4. 4.
    Brandes, U., Pich, C.: More flexible radial layout. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 107–118. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Brélaz, D.: New methods to color the vertices of a graph. Comm. ACM 22, 251–256 (1979)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bruckdorfer, T., Cornelsen, S., Gutwenger, C., Kaufmann, M., Montecchiani, F., Nöllenburg, M., Wolff, A.: Progress on partial edge drawings. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 67–78. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Brunel, E., Gemsa, A., Krug, M., Rutter, I., Wagner, D.: Generalizing geometric graphs. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 179–190. Springer, Heidelberg (2011)Google Scholar
  8. 8.
    Buchheim, C., Chimani, M., Gutwenger, C., Jünger, M., Mutzel, P.: Crossings and planarization. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press (2013)Google Scholar
  9. 9.
    Chrobak, M., Nishizeki, T.: Improved edge-coloring algorithms for planar graphs. J. Algo. 11(1), 102–116 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F.: h-quasi planar drawings of bounded treewidth graphs in linear area. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 91–102. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F.: Area requirement of graph drawings with few crossings per edge. Comp. Geom. 46(8), 909–916 (2013)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Didimo, W., Liotta, G.: The crossing angle resolution in graph drawing. In: Pach, J. (ed.) Thirty Essays on Geometric Graph Theory. Springer (2012)Google Scholar
  13. 13.
    Didimo, W., Montecchiani, F.: Fast layout computation of hierarchically clustered networks: Algorithmic advances and experimental analysis. In: IV 2012, pp. 18–23 (2012)Google Scholar
  14. 14.
    Dillencourt, M.B., Eppstein, D., Hirschberg, D.S.: Geometric thickness of complete graphs. Jour. Graph. Alg. and Appl. 4(3), 5–17 (2000)MathSciNetMATHGoogle Scholar
  15. 15.
    Duncan, C.A., Eppstein, D., Kobourov, S.G.: The geometric thickness of low degree graphs. In: SoCG 2004, pp. 340–346. ACM (2004)Google Scholar
  16. 16.
    Frick, A., Ludwig, A., Mehldau, H.: A fast adaptive layout algorithm for undirected graphs. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 388–403. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  17. 17.
    Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exper. 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  18. 18.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. PNAS 99(12), 7821–7826 (2002)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Hachul, S., Jünger, 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
  20. 20.
    Holyer, I.: The NP-completeness of edge-coloring. SIAM J. Comput. 10(4), 718–720 (1981)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Inf. Process. Lett. 31(1), 7–15 (1989)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Knuth, D.E.: The Stanford Graphbase: A Platform for Combinatorial Computing. Addison-Wesley Professional (1993)Google Scholar
  23. 23.
    Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4) (2008)Google Scholar
  24. 24.
    Michael Fire, Y.E., Puzis, R.: Organization mining using online social networks (2012), http://proj.ise.bgu.ac.il/sns
  25. 25.
    Mutzel, P., Jünger, M., Leipert, S. (eds.): GD 2001. LNCS, vol. 2265. Springer, Heidelberg (2002)MATHGoogle Scholar
  26. 26.
    Purchase, H.C.: Effective information visualisation: a study of graph drawing aesthetics and algorithms. Interact. Comput. 13(2), 147–162 (2000)CrossRefGoogle Scholar
  27. 27.
    Purchase, H.C., Carrington, D.A., Allder, J.-A.: Empirical evaluation of aesthetics-based graph layout. Empir. Softw. Eng. 7(3), 233–255 (2002)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Purchase, H.C., Hamer, J., Nöllenburg, M., Kobourov, S.G.: On the usability of lombardi graph drawings. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 451–462. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  29. 29.
    Shneiderman, B., Dunne, C.: Interactive network exploration to derive insights: Filtering, clustering, grouping, and simplification. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 2–18. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  30. 30.
    van Ham, F., van Wijk, J.J.: Interactive visualization of small world graphs. In: InfoVis 2004, pp. 199–206. IEEE (2004)Google Scholar
  31. 31.
    Vizing, V.G.: On an estimate of the chromatic class of a p-graph. Diskret. Analiz No. 3, 25–30 (1964)MathSciNetGoogle Scholar
  32. 32.
    Zhou, H., Xu, P., Yuan, X., Qu, H.: Edge bundling in information visualization. Tsinghua Science and Technology 18(2), 145–156 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Fabrizio Montecchiani
    • 1
  • Ioannis G. Tollis
    • 2
  1. 1.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di PerugiaItaly
  2. 2.Institute of Computer Science-FORTHUniv. of CreteGreece

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