Generalizations of Stress-Based Graph Layout to Non-Euclidean Geometries

Abstract

There exists many algorithms to compute node-link diagrams for graph visualization.Almost all of these algorithms aim to draw the graph in the flat Euclidean plane, but there are potentially good reasons to draw graphs in non-Euclidean geometries. Spherical geometry has no absolute center in any drawing, allowing any point to be moved centrally and inherits user familiarity with map and globe visualizations. Hyperbolic geometry creates a focus+context effect, with high detail in the center of the drawing and lower detail on the periphery. Additionally, it is possible to achieve better quality metrics for some graphs in non-Euclidean spaces. In this dissertation, we first introduce non-Euclidean geometry and survey it’s history in graph visualization. We then investigate how one can efficiently draw graphs in Euclidean and non-Euclidean spaces. Finally, we conduct a human subjects study to observe how these non-Euclidean visualizations perform with respect to task support.