Graphs are commonly used visualization tools in a variety of fields. Algorithms have been proposed that claim to improve the readability of graphs by reducing edge crossings, adjusting edge length, or some other means. However, little research has been done to determine which of these algorithms best suit human perception for particular graph properties. This thesis explores four different graph properties: average local clustering coefficient (ALCC), global clustering coefficient (GCC), number of triangles (NT), and diameter. For each of these properties, three different graph layouts are applied to represent three different approaches to graph visualization: multidimensional scaling (MDS), force directed (FD), and tsNET. In a series of studies conducted through the crowdsourcing platform Amazon Mechanical Turk, participants are tasked with discriminating between two graphs in order to determine their just noticeable differences (JNDs) for the four graph properties and three layout algorithm pairs. These results are analyzed using previously established methods presented by Rensink et al. and Kay and Heer.The average JNDs are analyzed using a linear model that determines whether the property-layout pair seems to follow Weber's Law, and the individual JNDs are run through a log-linear model to determine whether it is possible to model the individual variance of the participant's JNDs. The models are evaluated using the R2 score to determine if they adequately explain the data and compared using the Mann-Whitney pairwise U-test to determine whether the layout has a significant effect on the perception of the graph property. These tests indicate that the data collected in the studies can not always be modelled well with either the linear model or log-linear model, which suggests that some properties may not follow Weber's Law. Additionally, the layout algorithm is not found to have a significant impact on the perception of some of these properties.

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. This study applies previously established methodologies for perceptual analysis to identify which graph drawing layout will help the user best perceive a particular graph property. A large scale (n = 588) crowdsourced experiment is conducted to investigate whether the perception of two graph properties (graph density and average local clustering coefficient) can be modeled using Weber’s law. Three graph layout algorithms from three representative classes (Force Directed - FD, Circular, and Multi-Dimensional Scaling - MDS) are studied, and the results of this experiment establish the precision of judgment for these graph layouts and properties. The 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.