Technical Foundations

Graph drawing software relies on a variety of mathematical results, mainly in graph theory , topology , and geometry , as well as computer science techniques, mainly in the areas algorithms and data structures, software engineering , and user interfaces. Many of the core techniques used in automatic graph drawing come from the intersection of mathematics and computer science in combinatorial and continuous optimization. Even though automatic graph drawing is a relatively young scientific field, a few generic approaches have emerged in the graph drawing community. They allow a classification of layout methods so that most software packages implement variations of such approaches. The purpose of this chapter is to lay the foundations for all subsequent chapters so that they can be read independently from each other while referring back to the common material presented here. This chapter has been written based on the requirements and the contributions of all authors in this book. This chapter is not an introduction to automatic graph drawing, because it is neither complete nor balanced. In order to avoid repetitions, we only explain subjects that are basic or used in at least two subsequent chapters. The following chapters contain a lot of additional material. For introductions into the field of automatic graph drawing we recommend the books “Graph Drawing” by Di Battista, Eades, Tamassia, and Tollis [23] and “Drawing Graphs” edited by Kaufmann and Wagner [52]. Nevertheless, this book is self-contained in the sense that after this chapter has been read, every subsequent chapter can be read without referring to external sources.