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Graph Layout and Graph Properties Perception Pants Need to Select the Graph with the Desired Property

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Graph Layout and Graph Properties Perception Pants Need to Select the Graph with the Desired Property EUROVIS 2020/ C. Garth, A. Kerren, and G. E. Marei Short Paper The Effect of Graph Layout on the Perception of Graph Properties E. Kypridemou1;2 , M. Zito1 and M. Bertamini2 {1Department of Computer Science 2Visual Perception Lab, Department of Psychological Sciences}, University of Liverpool, UK Abstract The way in which a graph is described visually is crucial for the understanding and analysis of its structure. In this study we explore how different drawing layouts affect our perception of the graph’s properties. We study the perception of connectivity, density, and tree-ness using four different layouts: the Circular, Grid, Planar and Spring layouts. Results show that some layouts are better than others when we need to decide whether a graph is a tree or is connected. More sophisticated algorithms, like Planar and Spring, facilitate our perception, while Circular and Grid layouts lead to performance not better than chance. However, when perceiving the density of a graph, no layout was found to be better than the others. CCS Concepts • Human-centered computing ! Graph drawings; Empirical studies in visualization; • Computing methodologies ! Perception; 1. Introduction We are surrounded by networks such as social networks, neural net- works or the Internet, which need to be understood and analyzed. Managers for example, need to make sense of networks to make decisions. According to Newman [New18], the visualization of a graph is the first step for analyzing its structure, since it allows us (a) Circular (b) Grid (c) Planar (d) Spring to instantly see important features of the graph. There are many graph drawing algorithms that generate such visual representations Figure 1: Exemplar stimuli (a) Circular (non-target graph, Con- [Tam13,BETT98]. These algorithms have specific constraints (such nectivity) (b) Grid (non-target graph, Tree) task (c) Planar (target as straight-line) and also try to optimize some visual characteristics graph, Connectivity) (d) Spring (target graph, Density). (or aesthetics) [Pur02] of the drawing that are found to affect the human perception of the graph [BRSG07,Pur97,PCJ95,WPCM02]. Our aim is to study the ability of humans to extract information when perceiving stimuli of low versus high density [ATCB15], and from graph drawings regarding specific properties of the depicted hence they need to be studied separately. While Soni et al. used graph. We are particularly interested in how the drawing of the graphs of order 100 for their experiments, we focus on smaller graphs affects our perception of the graph’s properties. graphs of 16 nodes each, which we expect to be perceived as struc- tures of relations, rather than as a global texture. 2. Related Work 3. Method Previous studies focused on the perception of graph visualizations mostly in terms of their aesthetics, usability and readability. Al- The aim of this study is to provide some first insight on how the dif- though there is a great amount of studies on the perception of ferent drawing layouts might affect the perception of specific graph node-link diagrams (see [YAD∗18] for a survey of empirical stud- properties of small graphs. Previous user studies in the field allowed ies), there is not much research on how humans extract information participants unlimited time to process the graph drawings and mea- about specific graph properties. Recently, Soni et al. published ‘the sured the reaction time and accuracy as dependent variables. In this first experiment designed to model humans’ ability to perceptually study we are trying to identify the basic perceptual mechanisms discriminate graph properties’ [SLH∗18]. and hence we have chosen to limit the presentation time to 3000 Our study extends the work of Soni et al. by investigating the per- milliseconds per trial. We implemented the two-alternative forced ception of properties of smaller graphs. Studies on visual percep- choice (2AFC) methodology, in which we present two alternative tion suggest that there are two independent mechanisms involved images, only one of which contains the target graph, and partici- c 2020 The Author(s) Eurographics Proceedings c 2020 The Eurographics Association. E. Kypridemou, M. Zito, & M. Bertamini / Graph Layout and Graph Properties Perception pants need to select the graph with the desired property. After test- Task / Property Graph Properties ing different variations of small graphs of 12 to 20 nodes on this very short presentation time, we fixed the order of our graphs to 16 Connectivity: n = m = 16. Forced to be planar. Always nodes. We also restricted our study to the class of planar graphs, in select the a non-tree, because m > 15. order to use a planar layout and examine the effect of edge cross- graph that is Target: Forced Non-target: The disjoint ings. connected to be connected. union of two connected We used two of the layouts used in Soni et al., namely the Force graphs of n0 = m0 = 8. Directed (or Spring) and the Circular, and we also included the Cir- cular and Grid layouts (see Figure1). We studied the properties of Tree: select the n = 16. Forced to be planar. Always con- Connectivity, Density and Trees (see Table1) using three experi- graph that is a nected. mental tasks, one for each property. We chose the properties such tree that the tasks are relatively easy to perform in such short presenta- Target: A tree Non-target: G1 plus an tion time and easy to explain to non-expert users. To avoid carry- G1 (m = n−1 = extra edge (m = 16, con- over effects, we counterbalanced task order by applying a Latin 15, connected) nected, has one cycle) square design. Participants were randomly assigned to one of the Density: select n = 16. Forced to be planar & connected. three experimental conditions of task order (group A, B, or C). the graph with Always a non-tree, because m > 15. We have taken into account the methodological challenges of the more edges the empirical studies on graph drawings perception [vLPW∗17, Target: G1 with Non-target: G1 plus two HEH08]. During our experimental design, specific consideration m = 16 extra edges (m = 18) was given on the generation of the images, taking into account any confounding variables. We rigorously designed the properties of the Table 1: Properties of graphs used for each task, where n is the graphs and their drawings. We also controlled the previous knowl- number of nodes and m the number of edges. edge of participants regarding graphs. Finally, we used a mixed de- sign of both quantitative and qualitative methods, by using a ques- tionnaire between the different parts of our experiment. 3.3. Stimuli Graphs Generation: All stimuli were drawings of planar graphs of 3.1. Participants 16 nodes. For each task we generated a pool of two hundred graphs with specific properties, so that half of them had the desired prop- Twenty-four first-year Psychology students (5 males, aged 18-26) erty (target graphs) and half did not (non-target graphs). Because took part in the study and were evenly distributed across the three all three properties of the study are related to each other, we tried experimental conditions of task order (groups A, B, C). They all to limit any effects from confounding variables by fixing as many reported a normal or corrected-to-normal vision and no previous properties as possible. Table1 gives a summary of the way we gen- knowledge about graphs. The experiment passed the local ethics erated the graphs and their properties. For Connectivity, we assume committee approval (PSYC-5698). One of the participants had very that the task becomes trivial when we have isolated nodes in the low score (29%) for the Tree task and we have decided to exclude graph. To avoid such cases, we restrict the class of non-connected his/her data for this task from our dataset. graphs to those of 2 connected components, with 8 nodes each. We force the two components to be of the same order, because other- wise the task becomes trivial again (e.g., a 2-node component forms 3.2. Apparatus and Procedure a line). For the Tree task, we decided to restrict the non-trees class Participants were tested individually in a quiet darkened room and to connected graphs with one cycle to keep connectivity across tar- head position was stabilized with a chin rest in a fixed distance of get and non-target graphs fixed, while minimizing the difference of 57 cm from a 15.6” laptop monitor with a 60 Hz refresh rate and a density between the two. 1920 × 1080 monitor resolution. The experiment comprised three Graphs Drawing: After generating the graphs, we used four algo- parts, one for each property. For each part, participants read rele- rithms for drawing them: Circular, Grid, Planar and Spring. This vant instructions describing the graph property and then the exper- resulted to a pool of eight hundred graph drawings for each task. imenter verbally explained the property and provided eight exam- The Circular and Grid layouts acted more as baseline layouts, in ple drawings. Then they performed a training session of 16 trials, the sense that the correspondence of nodes to points in space was during which auditory feedback was provided. Following the train- independent of the abstract graph: nodes were randomly allocated ing, participants provided feedback on how confident they were to the pre-selected positions on the plane. On the contrary, for both about their understanding of the property. In cases of low confi- the Planar and the Spring layouts, we used more sophisticated al- dence self-reports, the experimenter provided additional informa- gorithms and hence the topology of resulting drawings was highly tion. After ensuring that all was sufficiently explained, participants dependent on the graphs.
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