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

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

We present a multi-scale layout algorithm for the aesthetic drawing of undirected graphs with straight-line edges. The algorithm is extremely fast, and is capable of drawing graphs that are substantially larger than those we have encountered in prior work. For example, the paper contains a drawing of a graph with over 15,000 vertices. Also we achieve "nice" drawings of 1000 vertex graphs in about 1 second. The proposed algorithm embodies a new multi-scale scheme for drawing graphs, which was motivated by the earlier multi-scale algorithm of Hadany and Harel [HH99]. In principle, it could significantly improve the speed of essentially any force-directed method (regardless of that method's ability of drawing weighted graphs or the continuity of its cost-function).

We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of a million nodes in less than a minute. Moreover, the algorithm can deal with more general entities, such as graphs with masses and negative weights (to be defined in the text), and it appears to be applicable outside of graph drawing too.

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 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.

. We report on our experiments with five graph drawing algorithms for general undirected graphs. These are the algorithms FR introduced by Fruchterman and Reingold [5], KK by Kamada and Kawai [11], DH by Davidson and Harel [1], Tu by Tunkelang [13] and GEM by Frick, Ludwig and Mehldau [6]. Implementations of these algorithms have been integrated into our GraphEd system [9]. We have tested these algorithms on a wide collection of examples and with different settings of parameters. Our examples are from original papers and by our own. The obtained drawings are evaluated both empirically and by GraphEd's evaluation toolkit. As a conclusion we can confirm the reported good behaviour of the algorithms. Combining time and quality we recommend to use GEM or KK first, then FR and Tu and finally DH. 1 Introduction Graph drawing has become an important area of research in Computer Science. There is a wide range of applications including data structures, data bases, software engineering, VLSI te...

Dynamic graph layout refers to the layout of graphs that change over time. These changes are due to user interaction, algorithms, or other underlying processes determining the graph. Typically, users spend a noteworthy amount of time to get familiar with a layout, i.e.