Stress in a graph drawing has been a popular layout principle for more than two decades. Low stress drawings exhibit the property that the geometric distances between all pairs of nodes correlate with the shortest paths between them. The assumption has always been that low stress drawings are "nicer" and better support human perception and comprehension than high stress drawings. In this paper, we put these assumptions to the test. We use a normalised scale-independent and rotation-independent metric for stress; this is necessary to ensure strict controls on our experimental stimuli. We report on three experiments, exploring human perception of stress, preference for stress, and the effect of stress on a graph performance task. We conclude that people can see stress in a graph drawing, that they prefer low stress drawings, and that their performance in a shortest path task improves as stress decreases - thus empirically confirming long-standing assumptions.

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.

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.

Any graph drawing can be characterised by a range of computational aesthetic metrics. For example, a given drawing might be described as having eight crossings, a mean angular resolution of 0.34, and an edge orthogonality value of 0.72. However, without knowing the distribution of these metrics it is hard to compare the quality of drawings of different graphs, nor know whether a given drawing is typical or an outlier within the space of all possible drawings. This paper explores the range and distribution of ten normalised graph drawing layout metrics, based on graphs created by six graph generation algorithms and drawings created by six popular layout algorithms. We include the "Rome" and "North" graph repositories in our analysis. Our exploration of the multi-dimensional aesthetics space allows for comparisons between the graph drawing algorithms, highlighting those that cover larger or smaller volumes of the aesthetics space. We calculate the correlation coefficients between the metrics, indicating those that may conflict with each other (negatively correlated), and those that may be redundant (positively correlated). Our results will be useful as the basis for simulated annealing or gradient descent layout algorithms, for identifying the best layout algorithms for producing a specified combination and range of aesthetics, and for informing experimental controls in human empirical studies.