We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is expressed as a generalized eigenvalue problem, which is solved rapidly using a novel algebraic multigrid technique. The same generalized eigenvalue problem seems to come up also in other fields, hence ACE appears to be applicable outside graph drawing too.

A new method for the visualization of huge hierarchical data structures is presented. The method is based on the observation that we can easily see the branches, leaves, and their arrangement in a botanical tree, despite of the large number of elements. The strand model of Holton is used to convert an abstract tree into a geometric model. Nonleaf nodes are mapped to branches and child nodes to subbranches. A naive application of this model leads to unsatisfactory results, hence it is tailored to suit our purposes better. Continuing branches are emphasized, long branches are contracted, and sets of leaves are shown as fruit. The method is applied to the visualization of directory structures. The elements, directories and files, as well as their relations can easily be extracted, thereby showing that the use of methods from botanical modeling can be effective for information visualization.

Two tasks in Graph Visualization require partitioning: the assignment of visual attributes and divisive clustering. Often, we would like to assign a color or other visual attributes to a node or edge that indicates an associated value. In an application involving divisive clustering, we would like to partition the graph into subsets of graph elements based on metric values in such a way that all subsets are evenly populated. Assuming a uniform distribution of metric values during either partitioning or coloring can have undesired effects such as empty clusters or only one level of emphasis for the entire graph. Probability density functions derived from statistics about a metric can help systems succeed at these tasks. CR Categories and Subject Descriptors: I.3.6 [Computer Graphics]: Methodology and Techniques -- Interaction Techniques; I.3.8 [Computer Graphics]: Applications Additional Keywords: graph visualization, graph navigation, metrics, clustering 1. INTRODUCTION A key issue...

GraphXML is a graph description language in XML that can be used as an interchange format for graph drawing and visualization packages. The generality and rich features of XML make it possible to define an interchange format that not only supports the pure, mathematical description of a graph, but also the needs of information visualization applications that use graph–based data structures.

GraphXML is a graph description language in XML that can be used as an interchange format for graph drawing and visualization packages. The generality and rich features of XML make it possible to define an interchange format that not only supports the pure, mathematical description of a graph, but also the needs of information visualization applications that use graph--based data structures. 1999 ACM Computing Classification System: D.2.12, H.3.5, I.3.6, I.3.8, I.7.2, Keywords and Phrases: information visualization, graph visualization, user interfaces, XML Note: The work was carried out under the project INS3.1 "Information Visualization". 1 INTRODUCTION GraphXML is a graph description language in XML * . The goal of GraphXML is to provide a general interchange format for graph drawing and visualization systems, and to connect those systems to other applications. The requirements of information visualization have greatly influenced design decisions during the development of Grap...

This report is broken down into four main sections, firstly giving the primary aims of the proposed research, followed by a review of background reading of present Information Visualisation (IV) techniques, which are categorised using an existing framework. This is followed by a description of the general visualisation problem we are concerned with plus a description of the specific area where such a visualisation could be of benefit. We then discuss the visualisation techniques that address situations that have the greatest similarity to our own problem, and explain why they still lack suitability for our purposes. Then, two prototypes that are under development are described, and the report finishes with a breakdown of proposed future work

The goal of this research is to study the role and effects of the use of animated information visualization in early stages of exploratory data analysis tasks. Despite the existence of a large body of research on information visualization, there has been little known regarding how and when one should use and how to interact with animated visualization to help exploring data. By animated visualization, we mean a type of information visualization technique that produces autonomous motions of representations. This research has explored the issue from two aspects: what cognitive effects animated information visualization has, and what interactions people would have with animated visualization when exploring data. We have conducted two user studies to investigate each aspect, and identified research challenges for designing an interactive animated information visualization environment that supports early stages of exploratory data analysis. These findings help us further study how to extend the notions developed in the spatial visualization to the temporal visualization; for instance, what Focus+Context means when applied to the time dimension in animated visualization. 1.

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It is often difficult for people, and particularly children, to learn relationships between data points (such as the relative sizes of the planets of the solar system). This sketch introduces a study aimed at investigating whether this type of data can be more easily learned by presenting it within a Virtual Environment, where the relationships between data points is represented by equivalent spatial relationships. By converting data relationships to spatial relationships, we are able to use our innate spatial abilities to understand and remember the data. The data is thus converted from an external form, to an internal representation that is always to hand and which is mentally easy to deal with.

Although graph drawing and graph visualisation have often been the subject of research, most of this research focuses on creating tidier drawings of relatively small graphs. However, in today’s complex society, research into the visualisation of large graphs is becoming increasingly important. One can think of maps of the entire internet or call graphs for very large software programs, for example. This thesis presents a visualisation method for a class of large graphs called state transition graphs. State transition graphs can be used as a mathematical description for processes or programs, and their analysis gives much insight into the process or program they describe. The major problem in the visualisation of large graphs is the size of the graph. Displaying an entire large graph all at once may overload the user with information, making it more difficult to comprehend. We attempt to overcome this problem by grouping nodes based on a local structural property. This reduces the complexity of the original graph and by initially displaying groups of nodes instead of individual nodes, the overall structure of the graph is revealed to the user. Further, instead of minimising the number of line crossings in a graph, as is often done in the visualisation of small graphs, we focus our attention on a different, global aesthetic aspect of a graph, namely symmetry. A clear picture of the symmetry in a graph allows the user to mentally split it into a number of smaller parts. Another advantage is that only one of the symmetrical parts has to be analysed, considerably reducing the amount of work necessary. After a description of the concepts behind this visualisation method, we present results obtained from working with a prototype. Finally, we discuss the advantages and disadvantages of this type of visualisation.