. 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...

JAWAA is a simple command language for creating animations of data structures and displaying them with a Web browser. Commands are stored in a script file that is retrieved and run by the JAWAA applet when the applet's Web page is accessed through the Web. JAWAA commands allow for creation and movement of primitive objects (circles, lines, text, rectangles) and data structure objects (arrays, stacks, queues, lists, trees and graphs). A JAWAA script can be generated as the output of a program written in any language. 1 Introduction An animation of a data structure is helpful to students as an educational aid in two ways, first as an alternative view in understanding a newly presented data structure or algorithm and second as an aid in debugging a program that uses the data structure. An animation can be easier to understand and remember than a textual representation, especially when one can interact with the animation by trying different input. Furthermore, using animations to debug p...

Spring algorithms are regarded as effective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric properties of graphs. This feature has been confirmed by numerous experiments. In this paper, firstly we formalize the concepts of graph symmetries in terms of "reflectional" and "rotational" automorphisms; and characterize the types of symmetries, which can be displayed simultaneously by a graph layout, in terms of "geometric" automorphism groups. We show that our formalization is complete. Secondly, we provide general theoretical evidence of why many spring algorithms can display graph symmetry. Finally, the strength of our general theorem is demonstrated from its application to several existing spring algorithms. 1 Introduction Graphs are commonly used in Computer Science to model relational structures such as programs, databases, and data structures. A good graph "layout" gives a clear understanding of a structural model; a ba...

Graphs are ubiquitous, finding applications in domains ranging from software engineering to computational biology. While graph theory and graph algorithms are some of the oldest, most studied fields in computer science, the problem of visualizing graphs is comparatively young. This problem, known as graph drawing, is that of transforming combinatorial graphs into geometric drawings for the purpose of visualization. Most published algorithms for drawing general graphs model the drawing problem with a physical analogy, representing a graph as a system of springs and other physical elements and then simulating the relaxation of this physical system. Solving the graph drawing problem involves both choosing a physical model and then using numerical optimization to simulate the physical system. In this

Algorithms based on force-directed placement and virtual physical models have become one of the most effective techniques for drawing undirected graphs. Spring-based algorithms that are the subject of this thesis are one type of force-directed algorithms. Spring algorithms are simple. They produce graphs with approximately uniform edge lengths, distribute nodes reasonably well, and preserve graph symmetries. A problem with these algorithms is that depending on their initial layout, it is possible that they find undesirable drawings associated with some local minimum criteria. In addition, it has always been a challenge to determine when a layout is stable in order to stop the algorithm. In this thesis, we develop a simple but effective cost function that can determine a node layout quality as well as the quality of the entire graph layout during the execution of a Spring algorithm. We use this cost function for producing the initial layout of the algorithm, for helping nodes move out ...

Abstract — Systems biologists use interaction graphs to model the behavior of biological systems at the molecular level. In an iterative process, such biologists observe the reactions of living cells under various experimental conditions, view the results in the context of the interaction graph, and then propose changes to the graph model. These graphs serve as a form of dynamic knowledge representation of the biological system being studied and evolve as new insight is gained from the experimental data. While numerous graph layout and drawing packages are available, these tools did not fully meet the needs of our immunologist collaborators. In this paper, we describe the data information display needs of these immunologists and translate them into design decisions. These decisions led us to create Cerebral, a system that uses a biologically guided graph layout and incorporates experimental data directly into the graph display. Small multiple views of different experimental conditions and a data-driven parallel coordinates view enable correlations between experimental conditions to be analyzed at the same time that the data is viewed in the graph context. This combination of coordinated views allows the biologist to view the data from many different perspectives simultaneously. To illustrate the typical analysis tasks performed, we analyze two datasets using Cerebral. Based on feedback from our collaborators we conclude that Cerebral is a valuable tool for analyzing experimental data in the context of an interaction graph model. Index Terms—Graph layout, systems biology visualization, small multiples, design study. 1

Suppose that G = (U; L; E) is a bipartite graph with vertex set U [L and edge set E U L. A typical convention for drawing G is to put the vertices of U on a horizontal line and the vertices of L on another horizontal line, and then to represent edges by line segments between the vertices that determine them. \Edge concentration" is known as an eective method to draw dense bipartite graphs clearly. The key in the edge concentration method is to reduce the number of edges, while the graph structural information is retained. The problem of having a maximal reduction on the number of edges by the edge concentration method was left open. In this paper we show that this problem is NP-hard. Keywords: Graph drawing, Bipartite graph, Edge cover, NP-complete. 1 Introduction Graphs are commonly used in computer science to model relation structures such as programs, databases, and data structures. A good graph drawing gives a clear understanding of a structural model; a bad drawing...

In visual datamining proximity data, which encodes the relationship between some entities as a distance, is often available. This proximity data is inherently high-dimensional and can be mapped into a low-dimensional 2D or 3D target space such that the points in the target space adhere to the specified distances. The target space can then be visualised as scatterplot.

We introduce the concept of coloring close and crossing edges in graph drawings with perceptually opposing colors making them individually more distinguishable and reducing edge-crossing effects. We define a “closeness ” metric on edges as a combination of distance, angle and crossing. We use the inverse of this metric to compute a color embedding in the L*a*b* color space and assign “close ” edges colors that are perceptually far apart. We present the following results: a distance metric on graph edges, a method of coloring graph edges, and anecdotal evidence that this technique can improve the reading of graph edges. Keywords--- graphs, colors, color embeddings. 1.

Recent empirical research has indicated that human graph reading performance improves when crossing angles increase. However, crossing angle has not been used as an aesthetic criterion for graph drawing algorithms so far. In this paper, we introduce a force-directed method that aims to construct graph drawings with large crossing angles. Experiments indicate that our method significantly increases crossing angles. Surprisingly, the experimental results further demonstrate that the resulting drawings produced by our method have fewer edge crossings, a shorter total edge length and more uniform edge lengths, compared to classical spring algorithms.