Drawing Graphs on the Sphere

Abstract

Graphs are most often visualized in the two dimensional Euclidean plane, but spherical space offers several advantages when visualizing graphs. First, some graphs such as skeletons of three dimensional polytopes (tetrahedron, cube, icosahedron) have spherical realizations that capture their 3D structure, which cannot be visualized as well in the Euclidean plane. Second, the sphere makes possible a natural "focus + context visualization with more detail in the center of the view and less details away from the center. Finally, whereas layouts in the Euclidean plane implicitly define notions of "central and "peripheral nodes, this issue is reduced on the sphere, where the layout can be centered at any node of interest. We first consider a projection-reprojection method that relies on transformations often seen in cartography and describe the implementation of this method in the GMap visualization system. This approach allows many different types of 2D graph visualizations, such as node-link diagrams, LineSets, BubbleSets and MapSets, to be converted into spherical web browser visualizations. Next we consider an approach based on spherical multidimensional scaling, which performs graph layout directly on the sphere. This approach supports node-link diagrams and GMap-style visualizations, rendered in the web browser using WebGL.