Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few timeslices can miss temporal features such as causality or even graph structure while too many timeslices slows the drawing computation. We present a model for dynamic graphs which is not based on timeslices, and a dynamic graph drawing algorithm, DynNoSlice, to draw graphs in this model. In our evaluation, we demonstrate the advantages of this approach over timeslicing on continuous data sets.
3D Graph Drawing. Several 2D algorithms have been extended to 3D. Bru and Frick @cite_30 proposed Gem3D , which extends Gem @cite_36 to 3D. Cruz and Twarog @cite_17 extended the simulated annealing approach of Davidson and Harel @cite_0 to 3D. Other algorithms work in both 2D and 3D, such as GRIP by Gajer and Kobourov @cite_21 . Munzner @cite_35 proposed an algorithm to draw directed graphs in a 3D hyperbolic space. Several other algorithms deal with particular constraints, such as orthogonal @cite_25 , or nested @cite_33 drawings. Cordeil 16Cordeil investigate the visualization of graphs in 3D using immersive environments.
@cite_30 @cite_35 @cite_33 @cite_36 @cite_21 @cite_0 @cite_25 @cite_17
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A recent trend in graph drawing is directed to the visualization of graphs in 3D [1, 5, 6]. A promising research direction concerns the extension of proven 2D techniques to 3D. We present a system extending the simulated annealing algorithm of Davidson and Harel [2] for straight-line two-dimensional drawings of general undirected graphs to three dimensions. This system features an advanced 3D user interface that assists the user in choosing and modifying the cost function and the optimization components on-line. 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 exponential amount 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. We demonstrate the H3Viewer graph drawing library, which can be run from a standalone program or in conjunction with other programs such as SGI's Site Manager application. Our layout and drawing algorithms support interactive navigation of large graphs up to 100,000 edges. We present an adaptive drawing algorithm with a guaranteed frame rate. Both layout and navigation occur in 3D hyperbolic space, which provides a view of a large neighborhood around an easily changeable point of interest. We find an appropriate spanning tree to use as the backbone for fast layout and uncluttered drawing, and non-tree links can be displayed on demand. Our methods are appropriate when node or link annotations can guide the choice of a good parent from among all of the incoming links. Such annotations can be constructed using only a small amount of domain-specific knowledge, thus rendering tractable many graphs which may seem rather densely connected at first glance. Drawing graphs as nodes connected by links is visually compelling but computationally difficult. Hyperbolic space and spanning trees can reduce visual clutter, speed up layout, and provide fluid interaction. This article briefly describes a software system that explicitly attempts to handle much larger graphs than previous systems and support dynamic exploration rather than final presentation. It then discusses the applicability of this system to goals beyond simple exploration. A software system that supports graph exploration should include both a layout and an interactive drawing component. I have developed new algorithms for both layout and drawing (H3 and H3Viewer). The H3Viewer drawing algorithm remains under development, so this article presents preliminary results. I have implemented a software library that uses these algorithms. It can handle graphs of more than 100,000 edges by using a spanning tree as the backbone for the layout and drawing algorithms.