The Perception of Stress in Graph Drawings

TL;DR

This paper investigates whether people can perceive the stress in graph drawings, a key aesthetic principle linked to the geometric and structural properties of the graph, and finds that novices can be trained to recognize it.

Contribution

It demonstrates that stress perception in graph drawings, a complex structural aesthetic, can be learned by novices through training, despite its reliance on underlying graph structure.

Findings

People can perceive stress in graph drawings.

Training enables novices to recognize stress.

Stress perception is accessible without understanding the formal definition.

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.