We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, high-quality static and dynamic layout algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools.

One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS community for more than two decades. It appears that majorization has advantages over the technique of Kamada and Kawai in running time and stability. We also present a few extensions to the basic energy model which can improve layout quality and computation speed in practice. Majorization-based optimization is essential to these extensions.

this article. Section 2 gives an overview of how a user operates the XGvis system. Section 3 deals with algorithm animation, direct manipulation and perturbation of the con guration. Section 4 gives details about the cost functions and their interactively controlled parameters for transformation, subsetting and weighting of dissimilarities. Section 5 describes diagnostics for MDS. Section 6 is about computational and systems aspects, including coordination of windows, algorithms, and large data problems. Finally, Section 7 gives a tour of applications with examples of proximity analysis, dimension reduction, and graph layout in two and more dimensions

We present a novel sampling-based approximation technique for classical multidimensional scaling that yields an extremely fast layout algorithm suitable even for very large graphs. It produces layouts that compare favorably with other methods for drawing large graphs, and it is among the fastest methods available. In addition, our approach allows for progressive computation, i.e. a rough approximation of the layout can be produced even faster, and then be refined until satisfaction.

Although there is extensive research on drawing graphs, none of the published methods are satisfactory for drawing general undirected graphs. Generating drawings which are optimal with respect to several aesthetic criteria is known to be NP-hard, so all published approaches to the problem have used heuristics. These heuristics are too slow to be practical for graphs of moderate size, and they do not produce consistently good drawings for general graphs. Moreover, they rely on general optimization methods, because problem-specific methods require a deeper theoretical understanding of the graph drawing problem. This paper presents an algorithm to generate two-dimensional drawings of undirected graphs. The algorithm uses a combination of heuristics to obtain drawings which are near-optimal with respect to an aesthetic cost function. The algorithm is incremental in nature, but preprocesses the graph to determine an order for node placement. The algorithm uses a local optimization strategy...

INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computer-aided-design. Research on graph drawing has been conducted within several diverse areas, including discrete mathematics (topological graph theory, geometric graph theory, order theory), algorithmics (graph algorithms, data structures, computational geometry, vlsi), and human-computer interaction (visual languages, graphical user interfaces, software visualization). This chapter overviews aspects of graph drawing that are especially relevant to computational geometry. Basic definitions on drawings and their properties are given in Section 1.1. Bounds on geometric and topological properties of drawings (e.g., area and crossings) are presented in Section 1.2. Section 1.3 deals with the time complexity of fundamental graph drawin

Graphviz is a collection of software for viewing and manipulating abstract graphs. It provides graph visualization for tools and web sites in domains such as software engineering, networking, databases, knowledge representation, and bio-informatics. Hundreds of thousands of copies have been distributed under an open source license. The core of Graphviz consists of implementations of various common types of graph layout. These layouts can be used via a C library interface, streambased command line tools, graphical user interfaces and web browsers. Aspects which distinguish the software include a retention of stream-based interfaces in conjunction with a variety of tools for graph manipulation, and support for a wide assortment of graphical features and output formats. The former makes it possible to write high-level programs for querying, modifying and displaying graphs. The latter allows Graphviz to be useful in a wide range of areas, with applications far removed from academic exercises. The algorithms of Graphviz concentrate on static layouts. Dynagraph is a sibling of Graphviz, with algorithms and interactive programs for incremental layout. At the library level, it provides an object-oriented interface for graphs and graph algorithms.

Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of user-defined constraints. 1.

In numerous application areas, general undirected graphs need to be drawn, and force-directed layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity. We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand.

In recent years there has been a resurgence of interest in nonlinear dimension reduc-tion methods. Among new proposals are so-called “Local Linear Embedding ” (LLE) and “Isomap”. Both use local neighborhood information to construct a global low-dimensional embedding of a hypothetical manifold near which the data fall. In this paper we introduce a family of new nonlinear dimension reduction methods called “Local Multidimensional Scaling ” or LMDS. Like LLE and Isomap, LMDS only uses local information from user-chosen neighborhoods, but it differs from them in that it uses ideas from the area of “graph layout”. A common paradigm in graph layout is to achieve desirable drawings of graphs by minimizing energy functions that balance attractive forces between near points and repulsive forces between non-near points against each other. We approach the force paradigm by proposing a parametrized family of stress or energy functions inspired by Box-Cox power transformations. This family provides users with considerable flexibility for achieving desirable embeddings, and it comprises most energy functions proposed in the past.