The Perception of Graph Properties in Graph Layouts

Abstract

When looking at drawings of graphs, questions about graph density, community structures, local clustering and other graph properties may be of critical importance for analysis. While graph layout algorithms have focused on minimizing edge crossing, symmetry, and other such layout properties, there is not much known about how these algorithms relate to a user's ability to perceive graph properties for a given graph layout. In this study, we apply previously established methodologies for perceptual analysis to identify which graph drawing layout will help the user best perceive a particular graph property. We conduct a large scale (n = 588) crowdsourced experiment to investigate whether the perception of two graph properties (graph density and average local clustering coefficient) can be modeled using Weber's law. We study three graph layout algorithms from three representative classes (Force Directed -FD, Circular, and Multi-Dimensional Scaling -MDS), and the results of this experiment establish the precision of judgment for these graph layouts and properties. Our findings demonstrate that the perception of graph density can be modeled with Weber's law. Furthermore, the perception of the average clustering coefficient can be modeled as an inverse of Weber's law, and the MDS layout showed a significantly different precision of judgment than the FD layout.

Same Stats, Different Graphs: Exploring the Space of Graphs in Terms of Graph Properties

“…However, as graphs get larger, some graph drawing algorithms may not allow us to distinguish differences in properties between two graphs purely from their drawings. We recently studied how the perception properties, such as density and ACC, is affected by different graph drawing algorithms [57]. The results confirm the intuition that some drawing algorithms are more appropriate than others in aiding viewers to perceive differences between underlying graph properties.…”

“…In a recent study of the ability to perceive different graph properties, such as edge density and clustering coefficient in different types of graph layouts (e.g., force-directed, circular), we generated a large number of graphs with 100 vertices. Specifically, we generated graphs that vary in a controlled way in edge density and graphs that vary in a controlled way in the average clustering coefficient [57]. A post-hoc analysis of this data (http://vader.lab.asu.edu/GraphAnalytics/) reveals some interesting patterns among the properties listed in Table 1.…”

Preserving Minority Structures in Graph Sampling

“…The second group measures the similarity between the original and sampled graphs. Two popular metrics in this group are the Jaccard Index (JI) that measures the similarity by the size of intersections [20] and the number of connected components (NCC) that measures the similarity of graph connectivity [64]. Recently, visual perception factors are considered in graph sampling evaluation.…”

“…Indicators in this experiment were Kolmogorov-Smirnov distance (KSD) [52], skew divergence distance (SDD) [44], reciprocal of NCC (RCC) [64], and JI [20]. They are commonly used in graph sampling evaluations (Section 2.3).…”

Ten simple rules to create biological network figures for communication

“…This measure is then used as an optimization criterion for the layout algorithm (Fig 3). Most prominent layouts are force directed and interpret the given similarity measure as an attracting force for nodes, whereas graph layouts based on multidimensional scaling perform better for cluster detection [15]. Centrality is a design principle in which the center and periphery may represent metaphorically high relevance and secondary relevance, respectively.…”