H3: laying out large directed graphs in 3D hyperbolic space

Abstract

We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space. We can lay out much larger structures than can be handled using traditional techniques for drawing general graphs because we assume a hierarchical nature of the data. We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree. Links which are not part of the spanning tree do not influence the layout but can be selectively drawn by user request.The volume of hyperbolic 3-space increases exponentially, as opposed to the familiar geometric increase of euclidean 3-space. We exploit this exponentialamount of room by computing the layout according to the hyperbolic metric. We optimize the cone tree layout algorithm for 3D hyperbolic space by placing children on a hemisphere around the cone mouth instead of on its perimeter. Hyperbolic navigation affords a Focus+Context view of the structure with minimal visual clutter. We have successfully laid out hierarchies of over 20,000 nodes. Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees.

An Occlusion-Reduced 3D Hierarchical Data Visualization Technique

“…While several 2D-based tree or graph visualization techniques have aimed all-inone display of the whole data [1] [5], interactive 3D information visualization techniques are also useful for such data structures. ConeTree [8], InformationCube [7], and H3 [6] are typical famous interactive 3D techniques for visualizing trees or graphs. Again, such techniques may cause occlusion of 3D objects and degrade the readability, and interactive operations are necessary to visualize the invisible parts.…”

DAG Drawing from an Information Visualization Perspective

“…As a consequence, tree visualization have a wide variety of usage in information visualization. The advantages of relying on tree drawing algorithms has motivated many authors to base their visualization strategy on the extraction and layout of a spanning tree [7,8,13] to gain the efficiency of the tree layout. Also, interacting with the graph often translates into the necessity of redrawing it a large number of times over very small time intervals; under those conditions, relying on the efficiency of a tree layout algorithms is sometimes viewed as a mandatory choice.…”

Interactive visualization and navigation in large data collections using the hyperbolic space

“…Tamara Munzner developed another graph layout algorithm for the three-dimensional hyperbolic space [8]. While she gains much more space for the layout, the problem of more complex navigation (and viewport control) in 3D and, more serious, the problem of occlusion appears.…”