Abstract. In the creation of graph drawing algorithms and systems, designers claim that by producing layouts that optimise certain aesthetic qualities, the graphs are easier to understand. Such aesthetics include maximise symmetry, minimise edge crosses and minimise bends.A previous study aimed to validate these claims with respect to three aesthetics, using paper-based experiments [11]. The study reported here is superior in many ways: five aesthetics are considered, attempts are made to place a priority order on the relative importance of the aesthetics, the experiments are run on-line, and the ease of understanding the drawings is measured in time, as well as in the number of errors. In addition, greater consideration is given to the possible effect of confounding factors in the graph drawings.The results indicate that reducing the number of edge crosses is by far the most important aesthetic, while minimising the number of bends and maximising symmetry have a lesser effect. The effects of maximising the minimum angle between edges leaving a node and of fixing edges and nodes to an orthogonal grid are not statistically significant. This work is important since it helps to demonstrate to algorithm and system designers the aesthetic qualities most important for aiding human understanding, the most appropriate compromises to make when there is a conflict in aesthetics, and consequently, how to build more effective systems.

A large class of diagrams can be informally characterized as node–link diagrams. Typically nodes represent entities, and links represent relationships between them. The discipline of graph drawing is concerned with methods for drawing abstract versions of such diagrams. At the foundation of the discipline are a set of graph aesthetics (rules for graph layout) that, it is assumed, will produce graphs that can be clearly understood. Examples of aesthetics include minimizing edge crossings and minimizing the sum of the lengths of the edges. However, with a few notable exceptions, these aesthetics are taken as axiomatic, and have not been empirically tested. We argue that human pattern perception can tell us much that is relevant to the study of graph aesthetics including providing a more detailed understanding of aesthetics and suggesting new ones. In particular, we find the importance of good continuity (ie keeping multi-edge paths as straight as possible) has been neglected. We introduce a methodology for evaluating the cognitive cost of graph aesthetics and we apply it to the task of finding the shortest paths in spring layout graphs. The results suggest that after the length of the path the two most important factors are continuity and edge crossings, and we provide cognitive cost estimates for these parameters. Another important factor is the number of branches emanating from nodes on the path.

In this paper, we present the results of a human-computer interaction experiment that compared the performance of the animation of dynamic graphs to the presentation of small multiples and the effect that mental map preservation had on the two conditions. Questions used in the experiment were selected to test both local and global properties of graph evolution over time. The data sets used in this experiment were derived from standard benchmark data sets of the information visualization community. We found that small multiples gave significantly faster performance than animation overall and for each of our five graph comprehension tasks. In addition, small multiples had significantly more errors than animation for the tasks of determining sets of nodes or edges added to the graph during the same timeslice, although a positive time-error correlation coefficient suggests that, in this case, faster responses did not lead to more errors. This result suggests that, for these two tasks, animation is preferable if accuracy is more important than speed. Preserving the mental map under either the animation or the small multiples condition had little influence in terms of error rate and response time.

This paper reports two experiments relating to the design of Tactons (or tactile icons

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