There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Cytoscape is an open source software project for integrating biomolecular interaction networks with high-throughput expression data and other molecular states into a unified conceptual framework. Although applicable to any system of molecular components and interactions, Cytoscape is most powerful when used in conjunction with large databases of protein-protein, protein-DNA, and genetic interactions that are increasingly available for humans and model organisms. Cytoscape's software Core provides basic functionality to layout and query the network; to visually integrate the network with expression profiles, phenotypes, and other molecular states; and to link the network to databases of functional annotations. The Core is extensible through a straightforward plug-in architecture, allowing rapid development of additional computational analyses and features. Several case studies of Cytoscape plug-ins are surveyed, including a search for interaction pathways correlating with changes in gene expression, a study of protein complexes involved in cellular recovery to DNA damage, inference of a combined physical/functional interaction network for Halobacterium, and an interface to detailed stochastic/kinetic gene regulatory models.

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Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks

1 GAs: What Are They?.- 2 GAs: How Do They Work?.- 3 GAs: Why Do They Work?.- 4 GAs: Selected Topics.- 5 Binary or Float?.- 6 Fine Local Tuning.- 7 Handling Constraints.- 8 Evolution Strategies and Other Methods.- 9 The Transportation Problem.- 10 The Traveling Salesman Problem.- 11 Evolution Programs for Various Discrete Problems.- 12 Machine Learning.- 13 Evolutionary Programming and Genetic Programming.- 14 A Hierarchy of Evolution Programs.- 15 Evolution Programs and Heuristics.- 16 Conclusions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- References.

Genetic Algorithms + Data Structures = Evolution Programs

SUMMARY We present a modification of the spring-embedder model of Eades [ Congresses Numerantium, 42, 149–160, (1984)] for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm.

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Graph drawing by force-directed placement

Social Network Analysis

From the Publisher:
This book is designed to describe fundamental algorithmic techniques for constructing drawings of graphs. Suitable as a book or reference manual, its chapters offer an accurate, accessible reflection of the rapidly expanding field of graph drawing.

Graph Drawing: Algorithms for the Visualization of Graphs

A Heuristic for Graph Drawing

Several data presentation problems involve drawing graphs so that they are easy to read and understand. Examples include circuit schematics and diagrams for information systems analysis and design. In this paper we present a bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs. Research on this topic is spread over the broad spectrum of computer science. This bibliography constitutes a first attempt to encompass both theoretical and application-oriented papers from disparate areas.

Algorithms for drawing graphs: an annotated bibliography

Many models in software and information engineering use graph representations; examples are data flow diagrams, state transition diagrams, flow charts, PERT charts, organization charts, Petri nets and entity-relationship diagrams. The usefulness of these graph representations depends on the quality of the layout of the graphs. Automatic graph layout, which can release humans from graph drawing, is now available in several visualization systems. Most automatic layout facilities take a purely combinatorial description of a graph and produce a layout of the graph; these methods are called 'layout creation' methods. For interactive systems, another kind of layout is needed: a facility which can adjust a layout after a change is made by the user or by the application. Although layout adjustment is essential in interactive systems, most existing layout algorithms are designed for layout creation. The use of a layout creation method for layout adjustment may totally rearrange the layout and thus destroy the user's 'mental map' of the diagram; thus a set of layout adjustment methods, separate from layout creation methods, is needed. This paper discusses some layout adjustment methods and the preservation of the 'mental map' of the diagram. First, several models are proposed to make the concept of 'mental map' more precise. Then two kinds of layout adjustments are described. One is an algorithm for rearranging a diagram to avoid overlapping nodes, and the other is a method aimed at changing the focus of interest of the user without destroying the mental map. Next, some experience with visualization systems in which the techniques have been employed is also described.

Layout Adjustment and the Mental Map

Systems engineers have recently shown interest in algorithms for drawing directed graphs so that they are easy to understand and remember. Each of the commonly used methods has a step which aims to adjust the drawing to decrease the number of arc crossings. We show that the most popular strategy involves an NP-complete problem regarding the minimization of the number of arcs in crossings in a bipartite graph. The performance of the commonly employed “barycenter” heuristic for this problem is analyzed. An alternative method, the “median” heuristic, is proposed and analyzed. The new method is shown to compare favorably with the old in terms of performance guarantees. As a bonus, we show that the median heuristic performs well with regard to the total length of the arcs in the drawing.

Peter Eades

Papers

Graph Drawing: Algorithms for the Visualization of Graphs

A Heuristic for Graph Drawing

Algorithms for drawing graphs: an annotated bibliography

Layout Adjustment and the Mental Map

Edge crossings in drawings of bipartite graphs