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Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?

Authors Gavin J. Mooney , Tim Hegemann , Alexander Wolff , Michael Wybrow , Helen C. Purchase

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ACM Subject Classification
  • Human-centered computing → Graph drawings
Keywords
  • Graph drawing metrics
  • metric landscape
  • straight-line drawings
  • polyline drawings
  • curved drawings
  • automated extraction of graph drawings

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Abstract

Graphs are drawn for various purposes, and drawings are meant to display various features of a graph (such as planarity, Hamiltonicity). Still, there is a long history in measuring the quality of a graph drawing. Most of the metrics that have been implemented and used in large studies assume that graphs are drawn straight-line. Most of the studies use randomly generated graphs or one of very few existing benchmark sets that consist of graphs with a specific technical background (e.g., telecommunication networks).
In this paper, we extend ten commonly used metrics to node-link diagrams where edges can be curves or polygonal chains. We implement these measures and use them to evaluate a new collection of graph drawings that we have extracted from 27 proceedings of the Graph Drawing conference using an automated pipeline. We compare the "metrics landscape" of our new benchmark set, the GD-collection-v1, which seems to mostly contain manually drawn graphs, to the metric landscape of a benchmark set with randomly generated graphs and computer-generated straight-line drawings that has been used in a recent study [Mooney et al.; PacificVis 2024].
Comparing the GD-collection-v1 with the Mooney at al. dataset reveals a distinct metrics landscape: GD drawings come from much smaller graphs (median vertex number 11 vs. 48) and therefore attain higher medians on most readability metrics. For example, Neighbourhood Preservation (0.5 vs. 0.239) is markedly higher in the GD-collection-v1. We also find that a large proportion of extracted drawings contain curved and/or polygonal edges (57%), motivating the extended metric definitions.

Cite As Get BibTex

Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase. Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.30

Author Details

Gavin J. Mooney
  • Monash University, Melbourne, Australia
Tim Hegemann
  • Universität Würzburg, Germany
Alexander Wolff
  • Universität Würzburg, Germany
Michael Wybrow
  • Monash University, Melbourne, Australia
Helen C. Purchase
  • Monash University, Melbourne, Australia

Funding

  • Hegemann, Tim: Supported by BMFTR grant 01IS22012C.

Acknowledgements

We thank Sebastian Kempf for his contributions to Graph Harvester.

Supplementary Materials

References

  1. Reyan Ahmed, Felice De Luca, Sabin Devkota, Stephen G Kobourov, and Mingwei Li. Multicriteria scalable graph drawing via stochastic gradient descent, (SGD)². IEEE Trans. Vis. Comput. Graphics, 28(6):2388-2399, 2022. URL: https://doi.org/10.1109/TVCG.2022.3155564.
  2. Christopher Auer, Christian Bachmaier, Franz J. Brandenburg, Andreas Gleißner, and Josef Reislhuber. Optical graph recognition. J. Graph Algorithms Appl., 17(4):541-565, 2013. URL: https://doi.org/10.7155/JGAA.00303.
  3. Lowell W. Beineke, Ortrud R. Oellermann, and Raymond E. Pippert. The average connectivity of a graph. Discrete Math., 252(1):31-45, 2002. URL: https://doi.org/10.1016/S0012-365X(01)00180-7.
  4. Kris Coolsaet, Sven D'hondt, and Jan Goedgebeur. House of Graphs 2.0: A database of interesting graphs and more. Discret. Appl. Math., 325:97-107, 2023. URL: https://doi.org/10.1016/J.DAM.2022.10.013.
  5. Julius Deynet, Tim Hegemann, Sebastian Kempf, and Alexander Wolff. Graph Harvester. In Stefan Felsner and Karsten Klein, editors, Graph Drawing and Network Visualization (GD), volume 320 of LIPIcs, pages 58:1-58:3. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. Poster with software presentation. URL: https://doi.org/10.4230/LIPIcs.GD.2024.58.
  6. Giuseppe Di Battista, Ashim Garg, Giuseppe Liotta, Roberto Tamassia, Emanuele Tassinari, and Francesco Vargiu. An experimental comparison of four graph drawing algorithms. Comput. Geom., 7(5):303-325, 1997. URL: https://doi.org/10.1016/S0925-7721(96)00005-3.
  7. J. Joseph Fowler. Characterization of unlabeled radial level planar graphs. In David Eppstein and Emden R. Gansner, editors, Graph Drawing (GD), volume 5849 of LNCS, pages 81-93. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-11805-0_10.
  8. Thomas M. J. Fruchterman and Edward M. Reingold. Graph drawing by force-directed placement. Softw. Pract. Exper., 21(11):1129-1164, 1991. URL: https://doi.org/10.1002/spe.4380211102.
  9. Emden Gansner, Eleftherios Koutsofios, and Stephen North. Drawing graphs with dot. Technical report, AT&T Research, 2006. URL: https://archive.org/details/dotguide.
  10. Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart. Exploring network structure, dynamics, and function using NetworkX. In Gaël Varoquaux, Travis Vaught, and Jarrod Millman, editors, Python in Science Conference (SciPy), pages 11-15, 2008. Google Scholar
  11. Marcus Kaiser. Mean clustering coefficients: The role of isolated nodes and leafs on clustering measures for small-world networks. New J. Phys., 10(8):083042, 2008. URL: https://doi.org/10.1088/1367-2630/10/8/083042.
  12. Tomihisa Kamada and Satoru Kawai. An algorithm for drawing general undirected graphs. Inf. Process. Lett., 31(1):7-15, 1989. URL: https://doi.org/10.1016/0020-0190(89)90102-6.
  13. Sebastian Kempf, Markus Krug, and Frank Puppe. KIETA: key-insight extraction from scientific tables. Appl. Intell., 53(8):9513-9530, 2023. URL: https://doi.org/10.1007/S10489-022-03957-8.
  14. Steve Kieffer, Tim Dwyer, Kim Marriott, and Michael Wybrow. HOLA: Human-like Orthogonal Network Layout. IEEE Trans Vis. Comput. Graphics, 22(1):349-358, 2016. URL: https://doi.org/10.1109/TVCG.2015.2467451.
  15. Joseph B. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29:1-27, 1964. URL: https://doi.org/10.1007/BF02289565.
  16. Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase. GD-collection-v1. Dataset, (visited on 2025-11-10). URL: https://github.com/hegetim/gd-collection
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.25065
  17. Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase. GEG Encodes Graphs. Software, (visited on 2025-11-10). URL: https://github.com/gavjmooney/geg
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.25066
  18. Gavin J. Mooney, Helen C. Purchase, Michael Wybrow, and Stephen G. Kobourov. The multi-dimensional landscape of graph drawing metrics. In IEEE Pacific Vis. Conf. (PacificVis), pages 122-131, 2024. URL: https://doi.org/10.1109/PACIFICVIS60374.2024.00022.
  19. Gavin J. Mooney, Helen C. Purchase, Michael Wybrow, Stephen G. Kobourov, and Jacob Miller. The perception of stress in graph drawings. In Stefan Felsner and Karsten Klein, editors, Graph Drawing and Network Visualization (GD), volume 320 of LIPIcs, pages 21:1-21:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.GD.2024.21.
  20. Martin Nöllenburg, Sebastian Röder, and Markus Wallinger. GdMetriX - A NetworkX extension for graph drawing metrics. In Stefan Felsner and Karsten Klein, editors, Graph Drawing & Network Vis. (GD), volume 320 of LIPIcs, pages 45:1-45:3. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.GD.2024.45.
  21. Helen C. Purchase. Which aesthetic has the greatest effect on human understanding? In Giuseppe Di Battista, editor, Graph Drawing, volume 1353 of LNCS, pages 248-261. Springer, 1997. URL: https://doi.org/10.1007/3-540-63938-1_67.
  22. Helen C. Purchase. Metrics for graph drawing aesthetics. J. Vis. Lang. Comput., 13(5):501-516, 2002. URL: https://doi.org/10.1006/jvlc.2002.0232.
  23. Helen C. Purchase, Robert F. Cohen, and Murray James. Validating graph drawing aesthetics. In G. Goos, J. Hartmanis, J. van Leeuwen, and Franz J. Brandenburg, editors, Graph Drawing, volume 1027 of LNCS, pages 435-446. Springer, 1996. URL: https://doi.org/10.1007/BFb0021827.
  24. Marcel Radermacher, Klara Reichard, Ignaz Rutter, and Dorothea Wagner. A geometric heuristic for rectilinear crossing minimization. In Workshop Algorithm Engin. & Exper. (ALENEX), pages 129-138. SIAM, 2018. URL: https://doi.org/10.1145/3325861.
  25. Kiran Smelser, Jacob Miller, and Stephen Kobourov. "Normalized stress" is not normalized: How to interpret stress correctly. ArXiv preprint, 2024. URL: https://doi.org/10.48550/arXiv.2408.07724.
  26. Kozo Sugiyama, Shojiro Tagawa, and Mitsuhiko Toda. Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cybern., 11:109-125, 1981. URL: https://doi.org/10.1109/TSMC.1981.4308636.
  27. GraphML Team. The graphml file format, 2002. URL: http://graphml.graphdrawing.org/.
  28. Colin Ware, Helen Purchase, Linda Colpoys, and Matthew McGill. Cognitive Measurements of Graph Aesthetics. Inform. Vis., 1(2):103-110, 2002. URL: https://doi.org/10.1057/palgrave.ivs.9500013.
  29. Erik Welch and Stephen Kobourov. Measuring symmetry in drawings of graphs. Comput. Graph. Forum, 36(3):341-351, 2017. URL: https://doi.org/10.1111/cgf.13192.
  30. Minfeng Zhu, Wei Chen, Yuanzhe Hu, Yuxuan Hou, Liangjun Liu, and Kaiyuan Zhang. DRGraph: An efficient graph layout algorithm for large-scale graphs by dimensionality reduction. IEEE Trans. Vis. Comput. Graphics, 27(2):1666-1676, 2021. URL: https://doi.org/10.1109/TVCG.2020.3030447.
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