this paper, we introduce an algorithm that attempts to produce aesthetically-pleasing, two-dimensional pictures of graphs by doing simplified simulations of physical systems. We are concerned with drawing undirected graphs according to some generally accepted aesthetic criteria: 1. Distribute the vertices evenly in the frame. 2. Minimize edge crossings. 3. Make edge lengths uniform. 4. Reflect inherent symmetry. 5. Conform to the frame. Our algorithm does not explicitly strive for these goals, but does well at distributing vertices evenly, making edge lengths uniform, and reflecting symmetry. Our goals for the implementation are speed and simplicity. PREVIOUS WORK Our algorithm for drawing undirected graphs is based on the work of Eades which, in turn, evolved from a VLSI technique called force-directed placement

Never before in history has data been generated at such high volumes as it is today. Exploring and analyzing the vast volumes of data is becoming increasingly difficult. Information visualization and visual data mining can help to deal with the flood of information. The advantage of visual data exploration is that the user is directly involved in the data mining process. There are a large number of information visualization techniques which have been developed over the last decade to support the exploration of large data sets. In this paper, we propose a classification of information visualization and visual data mining techniques which is based on the data type to be visualized, the visualization technique, and the interaction and distortion technique. We exemplify the classification using a few examples, most of them referring to techniques and systems presented in this special section.

Embedding of a graph metric in Euclidean space efficiently and accurately is an important problem in general with applications in topology aggregation, closest mirror selection, and application level routing. We propose a new graph embedding scheme called Big-Bang Simulation (BBS), which simulates an explosion of particles under force field derived from embedding error. BBS is shown to be significantly more accurate, compared to all other embedding methods including GNP. We report an extensive simulation study of BBS compared with several known embedding schemes and show its advantage for distance estimation (as in the IDMaps project), mirror selection and topology aggregation.

Abstract. We present a randomized adaptive layout algorithm for nicely drawing undirected graphs that is based on the spring-embedder paradigm and contains several new heuristics to improve the convergence, including local temperatures, gravitational forces and the detection of rotations and oscillations. The proposed algorithm achieves drawings of high quality on a wide range of graphs with standard settings. Moreover, the algorithm is fast, being thus applicable on general undirected graphs of substantially larger size and complexity than before [9, 6, 3]. Aesthetically pleasing solutions are found in most cases. We give empirical data for the running time of the algorithm and the quality of the computed layouts. 1

We have been collecting and recording routing paths from a test host to each of over 90,000 registered networks on the Internet since August 1998. The resulting database contains interesting routing and reachability information, and is available to the public for research purposes. The daily scans cover approximately a tenth of the networks on the Internet, with a full scan run roughly once a month. We have also been collecting Lucent's intranet data, and applied these tools to understanding its size and connectivity. We have also detecting the loss of power to routers in Yugoslavia as the result of NATO bombing. A simulated spring-force algorithm lays out the graphs that results from these databases. This algorithm is well known, but has never been applied to such a large problem. The Internet graph, with around 88,000 nodes and 100,000 edges, is much larger than those previously considered tractable by the data visualization community. The resulting Internet layouts are pleasant, though rather cluttered. On smaller networks, like Lucent's intranet, the layouts present the data in a useful way. For the Internet data, we have tried plotting a minimum distance spanning tree; by throwing away edges, the remaining graph can be made more accessible. Once a layout is chosen, it can be colored in various ways to show network-relevant data, such as IP address, domain information, location, ISPs, location of firewalls, etc. This paper expands and updates the description of the project given in [2]. 1

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm.

We describe Gevol, a system that visualizes the evolution of software using a novel graph drawing technique for visualization of large graphs with a temporal component. Gevol extracts information about a Java program stored within a CVS version control system and displays it using a temporal graph visualizer. This information can be used by programmers to understand the evolution of a legacy program: Why is the program structured the way it is? Which programmers were responsible for which parts of the program during which time periods? Which parts of the program appear unstable over long periods of time and may need to be rewritten? This type of information will complement that produced by more static tools such as source code browsers, slicers, and static analyzers. 1

In this paper we present an extensive experimental study comparing four general-purpose graph drawing algorithms. The four algorithms take as input general graphs (with no restrictions whatsoever on connectivity, planarity, etc.) and construct orthogonal grid drawings, which are widely used in software and database visualization applications. The test data (available by anonymous ftp) are 11,582 graphs, ranging from 10 to 100 vertices, which have been generated from a core set of 112 graphs used in "real-life" software engineering and database applications. The experiments

We introduce a new method to optimize the required area, minimum angle and number of bends of planar drawings of graphs on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear time and space algorithms can be designed for many graph drawing problems. -- Every triconnected planar graph G can be drawn convexly with straight lines on an (2n \Gamma 4) \Theta (n \Gamma 2) grid, where n is the number of vertices. -- Every triconnected planar graph with maximum degree four can be drawn orthogonally on an n \Theta n grid with at most d 3n 2 e + 4, and if n ? 6 then every edge has at most two bends. -- Every 3-planar graph G can be drawn with at most b n 2 c + 1 bends on an b n 2 c \Theta b n 2 c grid. -- Every triconnected planar graph G can be drawn planar on an (2n \Gamma 6) \Theta (3n \Gamma 9) grid with minimum angle larger than 2 d radians and at most 5n \Gamma 15 bends, with d the maximum d...

We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2-D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seconds. The new method appears to have several advantages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs.