Perception of Symmetries in Drawings of Graphs

  • Felice De LucaEmail author
  • Stephen Kobourov
  • Helen Purchase
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)


Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular. There are three main types of symmetry: reflective, translational, and rotational. We report the results of a human subjects experiment to determine what types of symmetries are more salient in drawings of graphs. We found statistically significant evidence that vertical reflective symmetry is the most dominant (when selecting among vertical reflective, horizontal reflective, and translational). We also found statistically significant evidence that rotational symmetry is affected by the number of radial axes (the more, the better), with a notable exception at four axes.



We thank Eric Welch for help with the experiment, Hang Chen for help with statistics, and yFiles for providing their software for research and education. This work is supported by NSF grants CCF-1423411 and CCF-1712119.


  1. 1.
    Bennett, C., Ryall, J., Spalteholz, L., Gooch, A.: The aesthetics of graph visualization. Comput. Aesthet. 2007, 57–64 (2007)Google Scholar
  2. 2.
    Bruce, V., Green, P.R., Georgeson, M.A.: Visual Perception: Physiology, Psychology, & Ecology. Psychology Press, Hove (2003)Google Scholar
  3. 3.
    Bruce, V.G., Morgan, M.J.: Violations of symmetry and repetition in visual patterns. Perception 4(3), 239–249 (1975)CrossRefGoogle Scholar
  4. 4.
    Bruckdorfer, T., Kaufmann, M.: Mad at edge crossings? break the edges!. In: Kranakis, E., Krizanc, D., Luccio, F. (eds.) FUN 2012. LNCS, vol. 7288, pp. 40–50. Springer, Heidelberg (2012). Scholar
  5. 5.
    Burch, M., Vehlow, C., Konevtsova, N., Weiskopf, D.: Evaluating partially drawn links for directed graph edges. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS, vol. 7034, pp. 226–237. Springer, Heidelberg (2012). Scholar
  6. 6.
    Cattaneo, Z., Bona, S., Silvanto, J.: Not all visual symmetry is equal: partially distinct neural bases for vertical and horizontal symmetry. Neuropsychologia 104, 126–132 (2017)CrossRefGoogle Scholar
  7. 7.
    Corballis, M.C., Roldan, C.E.: On the perception of symmetrical and repeated patterns. Percept. Psychophys. 16(1), 136–142 (1974)CrossRefGoogle Scholar
  8. 8.
    Eades, P., Hong, S.H.: Symmetric graph drawing. In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 87–113. Chapman and Hall/CRC, Boca Raton (2013)Google Scholar
  9. 9.
    Giannouli, V.: Visual symmetry perception. Encephalos 50, 31–42 (2013)Google Scholar
  10. 10.
    Jennings, B.J., Kingdom, F.A.A.: Searching for radial symmetry. i-Perception 8(4), 2041669517725758 (2017)CrossRefGoogle Scholar
  11. 11.
    Klapaukh, R.: An empirical evaluation of force-directed graph layout. Ph.D. thesis, Victoria University of Wellington (2014)Google Scholar
  12. 12.
    Lai, H.C., Chien, S.H.L., Kuo, W.Y.: Visual short-term memory for abstract patterns: effects of symmetry, element connectedness, and probe quadrant. J. Vis. 9(8), 593 (2009)CrossRefGoogle Scholar
  13. 13.
    Lemon, K., Allen, E.B., Carver, J.C., Bradshaw, G.L.: An empirical study of the effects of gestalt principles on diagram understandability. In: 2007 First International Symposium on Empirical Software Engineering and Measurement. ESEM 2007, pp. 156–165. IEEE (2007)Google Scholar
  14. 14.
    Marriott, K., Purchase, H., Wybrow, M., Goncu, C.: Memorability of visual features in network diagrams. IEEE Trans. Visual. Comput. Graph. 18(12), 2477–2485 (2012)CrossRefGoogle Scholar
  15. 15.
    Nesbitt, K.V., Friedrich, C.: Applying gestalt principles to animated visualizations of network data. In: 2002 6th International Conference on Information Visualisation, pp. 737–743. IEEE (2002)Google Scholar
  16. 16.
    Norman, D.A.: Emotion Design: Why We Love (or Hate) Everyday Things (2004)Google Scholar
  17. 17.
    Palmer, S.E.: Theoretical approaches to vision. In: Vision Science: Photons to Phenomenology, pp. 45–92 (1999)Google Scholar
  18. 18.
    Palmer, S.E., Hemenway, K.: Orientation and symmetry: effects of multiple, rotational, and near symmetries. J. Exp. Psychol. Hum. Percept. Perform. 4(4), 691–702 (1978)CrossRefGoogle Scholar
  19. 19.
    Purchase, H.: Metrics for graph drawing aesthetics. J. Vis. Lang. Comput. 13(5), 501–516 (2002)CrossRefGoogle Scholar
  20. 20.
    Purchase, H.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997). Scholar
  21. 21.
    Purchase, H.C., Cohen, R.F., James, M.: Validating graph drawing aesthetics. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 435–446. Springer, Heidelberg (1996). Scholar
  22. 22.
    Reddit: The front page of the internet.
  23. 23.
    Rock, I., Palmer, S.: The legacy of gestalt psychology. Sci. Am. 263(6), 84–91 (1990)CrossRefGoogle Scholar
  24. 24.
    Royer, F.L.: Detection of symmetry. J. Exp. Psychol. Hum. Percept. Perform. 7(6), 1186–1210 (1981)CrossRefGoogle Scholar
  25. 25.
    Rusu, A., Fabian, A.J., Jianu, R., Rusu, A.: Using the gestalt principle of closure to alleviate the edge crossing problem in graph drawings. In: 2011 15th International Conference on Information Visualisation, pp. 488–493. IEEE (2011)Google Scholar
  26. 26.
    Schnore, M., Partington, J.: Immediate memory for visual patterns: symmetry and amount of information. Psychon. Sci. 8(10), 421–422 (1967)CrossRefGoogle Scholar
  27. 27.
    Sun, D., Wong, K.: On evaluating the layout of UML class diagrams for program comprehension. In: 2005 Proceedings of 13th International Workshop on Program Comprehension. IWPC 2005, pp. 317–326. IEEE (2005)Google Scholar
  28. 28.
    Tversky, B.: Visuospatial reasoning. In: The Cambridge Handbook of Thinking and Reasoning, pp. 209–240 (2005)Google Scholar
  29. 29.
    Wagemans, J.: Detection of visual symmetries. Spat. Vis. 9(1), 9–32 (1995)CrossRefGoogle Scholar
  30. 30.
    Ware, C.: Information Visualization: Perception for Design. Elsevier, Amsterdam (2004)Google Scholar
  31. 31.
    Welch, E., Kobourov, : S.: Measuring symmetry in drawings of graphs, vol. 36, pp. 341–351. Wiley (2017)Google Scholar
  32. 32.
    yWorks: The diagramming company.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Felice De Luca
    • 1
    Email author
  • Stephen Kobourov
    • 1
  • Helen Purchase
    • 2
  1. 1.University of ArizonaTucsonUSA
  2. 2.University of GlasgowGlasgowUK

Personalised recommendations