Agraph is a simple, powerful, elegant abstraction with broad applicability in computer science and many related fields. Algorithms that operate on graphs see heavy use in both theoretical and practical contexts. Graphs have a very natural visual representation as nodes and connecting links arranged in space. Seeing this structure explicitly can aid tasks in many domains. Many people automatically sketch such a picture when thinking about small graphs, often including simple annotations. The pervasiveness of visual representations of small graphs testifies to their usefulness. On the other hand, although many large data sets can be expressed as graphs, few such visual representations exist. What causes this discrepancy? For one thing, graph layout poses a hard problem, 1 one that current tools just can’t overcome. Conventional systems often falter when handling hundreds of edges, and none can handle more than a few thousand edges. 2 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. However, nonvisual manipulation of graphs with 50,000 edges is commonplace, and much larger instances exist. We can consider the Web as an extreme example of a graph with many millions of nodes and edges. Although many individual Web sites stay quite small, a significant number have more than 20,000 documents. The Unix file system reachable from a single networked workstation might include more than 100,000 files scattered across dozens of gigabytes worth of remotely mounted disk drives. Computational complexity is not the only reason that software to visually manipulate large graphs has lagged behind software to computationally manipulate them. Many previous graph layout systems have focused on fine-tuning the layout of relatively small graphs in support of polished presentations. A graph drawing system that focuses on the interactive browsing of large graphs

. This paper introduces a novel approach to the drawing of threedimensional graphs: the geometric approach. Graphs are decomposed into building elements that can easily be drawn as a geometric shape. Those elements are linked together in order to form the final layout. The proposed algorithm, Geo3D, has been implemented in the Java language and has been used to produce VRML models of the input graphs. Introduction The most common approach to graph drawing is to set the position of each vertex of the graph so that the final layout would satisfy some predefined aesthetics [1]. For example, force-directed algorithms use the spring model in order to minimize edge crossing and to distribute nodes evenly; other algorithms build a layout minimizing a cost function that depends on edge distance, node distribution etc. [2] The first algorithms for the drawing of graphs in three dimensions applied the above approaches, successfully used in the two-dimensional domain, to the extended space [4] [...

We present IVORY, a newly developed, platform-independent framework for physics-based visualization. IVORY is especially designed for information visualization applications and multidimensional graph layout. It is fully implemented in Java 1.1 and its architecture features client-server setup, which allows to run the visualization even on thin clients. In addition, VRML 2.0 exports can be viewed by any VRML plugged-in WWW-browser. Individual visual metaphors are invoked into IVORY via an advanced plug-in mechanism, where plug-ins can be implemented by any experienced user. The configuration of IVORY is accomplished using a script language, called IVML. Some interactive visualization examples, such as the integration of an haptic interface illustrate the performance and versatility of our system. Our current implementation supports NT 4.0. 1 keywords: three-dimensional information visualization, physics-based graph layout, object-oriented visualization toolkit, multidimensional inform...

In this paper, we present a new hierarchical clustering and visualization algorithm called H-BLOB, which groups and visualizes cluster hierarchies at multiple levels-of-detail. Our method is fundamentally different to conventional clustering algorithms, such as C-means, K-means, or linkage methods that are primarily designed to partition a collection of objects into subsets sharing similar attributes. These approaches usually lack an efficient level-ofdetail strategy that breaks down the visual complexity of very large datasets for visualization. In contrast, our method combines grouping and visualization in a two stage process constructing a hierarchical setting. In the first stage a cluster tree is computed making use of an edge contraction operator. Exploiting the inherent hierarchical structure of this tree, a second stage visualizes the clusters by computing a hierarchy of implicit surfaces. We believe that HBLOB is especially suited for the visualization of very large datasets and for visual decision making in information visualization. The versatility of the algorithm is demonstrated using examples from visual data mining.

Visualization of similarity is an emerging technique for analyzing relation-based data sets. A common way of computing the respective layouts in an information space is to employ a physics-based mass-spring system. Force computation, however, is costly and of order N . In this paper, we propose a new acceleration method to adopt a well-known optimized force-computation algorithm which drastically reduces the computation time to the order of N log N. The basic idea is to derive a two-pass, "prediction and correction" procedure including a customized potential function. We have applied this method to two different applications: web access and sales analysis. Both demonstrate the efficiency and versatility of the presented method.

Graphs are often used to encapsulate relationship between objects. Graph drawing enables visualization of such relationships. The usefulness of this visual representation is dependent on whether the drawing is aesthetic. While there are no strict criteria for aesthetics of a drawing, it is generally agreed, for example,

Web transactions are multidimensional and have a number of attributes: client, URL, response times, and numbers of messages. One of the key questions is how to simultaneously lay out in a graph the multiple relationships, such as the relationships between the web client response times and URLs in a web access application. In this paper, we describe a freeze technique to enhance a physics-based visualization system for web transactions. The idea is to freeze one set of objects before laying out the next set of objects during the construction of the graph. As a result, we substantially reduce the force computation time. This technique consists of three steps: automated classification, a freeze operation, and a graph layout. These three steps are iterated until the final graph is generated. This iterated-freeze technique has been prototyped in several e-service applications at Hewlett Packard Laboratories. It has been used to visually analyze large volumes of service and sales transactions at online web sites.