Skip to main content

Shape-Faithful Graph Drawings

  • Conference paper
  • First Online:
Graph Drawing and Network Visualization (GD 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13764))

Included in the following conference series:

Abstract

Shape-based metrics measure how faithfully a drawing D represents the structure of a graph G, using the proximity graph S of D. While some limited graph classes admit proximity drawings (i.e., optimally shape-faithful drawings, where \(S = G\)), algorithms for shape-faithful drawings of general graphs have not been investigated.

In this paper, we present the first study for shape-faithful drawings of general graphs. First, we conduct extensive comparison experiments for popular graph layouts using the shape-based metrics, and examine the properties of highly shape-faithful drawings. Then, we present ShFR and ShSM, algorithms for shape-faithful drawings based on force-directed and stress-based algorithms, by introducing new proximity forces/stress. Experiments show that ShFR and ShSM obtain significant improvement over FR (Fruchterman-Reingold) and SM (Stress Majorization), on average 12% and 35% respectively, on shape-based metrics.

This work is supported by ARC grant DP190103301.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Di Battista, G., Lenhart, W., Liotta, G.: Proximity drawability: a survey extended abstract. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 328–339. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-58950-3_388

    Chapter  Google Scholar 

  2. Di Battista, G., Liotta, G., Whitesides, S.: The strength of weak proximity (extended abstract). In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 178–189. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0021802

    Chapter  Google Scholar 

  3. Bose, P., Lenhart, W., Liotta, G.: Characterizing proximity trees. Algorithmica 16(1), 83–110 (1996)

    Article  MathSciNet  Google Scholar 

  4. Chimani, M., Gutwenger, C., Jünger, M., Klau, G.W., Klein, K., Mutzel, P.: The open graph drawing framework (OGDF). In: Handbook of Graph Drawing and Visualization 2011, pp. 543–569 (2013)

    Google Scholar 

  5. Chrobak, M., Kant, G.: Convex grid drawings of 3-connected planar graphs. Int. J. Comput. Geom. Appl. 7(03), 211–223 (1997)

    Article  MathSciNet  Google Scholar 

  6. Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. (TOMS) 38(1), 1 (2011)

    MathSciNet  Google Scholar 

  7. Eades, P., Hong, S.H., Nguyen, A., Klein, K.: Shape-based quality metrics for large graph visualization. J. Graph Algorithms Appl. 21(1), 29–53 (2017)

    Article  MathSciNet  Google Scholar 

  8. Evans, W., Gansner, E.R., Kaufmann, M., Liotta, G., Meijer, H., Spillner, A.: Approximate proximity drawings. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS, vol. 7034, pp. 166–178. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-25878-7_17

    Chapter  Google Scholar 

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

    Google Scholar 

  10. Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic variation analysis. Syst. Zool. 18(3), 259–278 (1969)

    Article  Google Scholar 

  11. Gansner, E.R., Koren, Y., North, S.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31843-9_25

    Chapter  Google Scholar 

  12. 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). https://doi.org/10.1007/978-3-540-31843-9_29

    Chapter  Google Scholar 

  13. Hagberg, A., Swart, P., Chult, D.S.: Exploring network structure, dynamics, and function using networkx. Tech. rep., Los Alamos National Lab. (LANL), Los Alamos, NM (United States) (1 2008)

    Google Scholar 

  14. Hu, Y.: Efficient, high-quality force-directed graph drawing. Math. J. 10(1), 37–71 (2005)

    Google Scholar 

  15. Jaccard, P.: The distribution of the flora in the alpine zone. 1. New Phytol. 11(2), 37–50 (1912)

    Google Scholar 

  16. Kruiger, J.F., Rauber, P.E., Martins, R.M., Kerren, A., Kobourov, S., Telea, A.C.: Graph layouts by t-SNE. Comput. Graph. Forum 36(3), 283–294 (2017). https://doi.org/10.1111/cgf.13187

    Article  Google Scholar 

  17. Lenhart, W., Liotta, G.: Proximity drawings of outerplanar graphs (extended abstract). In: North, S. (ed.) GD 1996. LNCS, vol. 1190, pp. 286–302. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-62495-3_55

    Chapter  Google Scholar 

  18. Leskovec, J., Krevl, A.: SNAP Datasets: stanford large network dataset collection. http://snap.stanford.edu/data (Jun 2014)

  19. Liotta, G.: Proximity Drawings. chap. 4, pp. 115–154 (2013)

    Google Scholar 

  20. van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9(86), 2579–2605 (2008)

    Google Scholar 

  21. Meidiana, A., Hong, S.H., Eades, P.: Shape-faithful graph drawings (2022). https://arxiv.org/abs/2208.14095

  22. Noack, A.: An energy model for visual graph clustering. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 425–436. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24595-7_40

    Chapter  Google Scholar 

  23. Nocaj, A., Ortmann, M., Brandes, U.: Untangling the hairballs of multi-centered, small-world online social media networks. J. Graph Algorithms Appl. 19(2), 595–618 (2015). https://doi.org/10.7155/jgaa.00370

    Article  MathSciNet  Google Scholar 

  24. Preparata, F.P., Shamos, M.I.: Computational geometry: an introduction. Springer Science and Business Media, New York (2012). https://doi.org/10.1007/978-1-4612-1098-6

  25. Toth, C.D., O’Rourke, J., Goodman, J.E.: Handbook of Discrete and Computational Geometry. CRC Press, Boca Raton (2017)

    Google Scholar 

  26. Toussaint, G.T.: The relative neighbourhood graph of a finite planar set. Pattern Recogn. 12(4), 261–268 (1980)

    Article  MathSciNet  Google Scholar 

  27. Walker, J.Q.: A node-positioning algorithm for general trees. Softw. Pract. Experience 20(7), 685–705 (1990)

    Google Scholar 

  28. Wiese, R., Eiglsperger, M., Kaufmann, M.: yFiles - visualization and automatic layout of graphs. In: Jünger, M., Mutzel, P. (eds.) Graph Drawing Software. Mathematics and Visualization, pp. 173–191. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-642-18638-7_8

    Chapter  Google Scholar 

  29. Zheng, J.X., Pawar, S., Goodman, D.F.: Graph drawing by stochastic gradient descent. IEEE Trans. Visual. Comput. Graphics 25(9), 2738–2748 (2018)

    Article  Google Scholar 

  30. Zitnik, M., Sosič, R., Maheshwari, S., Leskovec, J.: BioSNAP Datasets: stanford biomedical network dataset collection. http://snap.stanford.edu/biodata (2018)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amyra Meidiana .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Meidiana, A., Hong, SH., Eades, P. (2023). Shape-Faithful Graph Drawings. In: Angelini, P., von Hanxleden, R. (eds) Graph Drawing and Network Visualization. GD 2022. Lecture Notes in Computer Science, vol 13764. Springer, Cham. https://doi.org/10.1007/978-3-031-22203-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22203-0_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22202-3

  • Online ISBN: 978-3-031-22203-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics