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The Perception of Stress in Graph Drawings

Authors Gavin J. Mooney , Helen C. Purchase , Michael Wybrow , Stephen G. Kobourov , Jacob Miller

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Gavin J. Mooney
  • Monash University, Melbourne, Australia
Helen C. Purchase
  • Monash University, Melbourne, Australia
Michael Wybrow
  • Monash University, Melbourne, Australia
Stephen G. Kobourov
  • Technical University of Munich, Campus Heilbronn, Germany
Jacob Miller
  • Technical University of Munich, Campus Heilbronn, Germany

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Gavin J. Mooney, Helen C. Purchase, Michael Wybrow, Stephen G. Kobourov, and Jacob Miller. The Perception of Stress in Graph Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.21

Abstract

Most of the common graph layout principles (a.k.a. "aesthetics") on which many graph drawing algorithms are based are easy to define and to perceive. For example, the number of pairs of edges that cross each other, how symmetric a drawing looks, the aspect ratio of the bounding box, or the angular resolution at the nodes. The extent to which a graph drawing conforms to these principles can be determined by looking at how it is drawn - that is, by looking at the marks on the page - without consideration for the underlying structure of the graph. A key layout principle is that of optimising "stress", the basis for many algorithms such as the popular Kamada & Kawai algorithm and several force-directed algorithms. The stress of a graph drawing is, loosely speaking, the extent to which the geometric distance between each pair of nodes is proportional to the shortest path between them - over the whole graph drawing. The definition of stress therefore relies on the underlying structure of the graph (the "paths") in a way that other layout principles do not, making stress difficult to describe to novices unfamiliar with graph drawing principles, and, we believe, difficult to perceive. We conducted an experiment to see whether people (novices as well as experts) can see stress in graph drawings, and found that it is possible to train novices to "see" stress - even if their perception strategies are not based on the definitional concepts.

Subject Classification

ACM Subject Classification
  • Human-centered computing → Empirical studies in visualization
Keywords
  • Stress
  • Graph Drawing
  • Visual Perception

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