By Rudolf Fleischer, Colin Hirsch (auth.), Michael Kaufmann, Dorothea Wagner (eds.)

Graph drawing includes all facets of visualizing structural kin among gadgets. the diversity of subject matters handled extends from graph conception, graph algorithms, geometry, and topology to visible languages, visible notion, and knowledge visualization, and to computer-human interplay and photographs layout. This monograph supplies a scientific assessment of graph drawing and introduces the reader lightly to the state-of-the-art within the zone. The presentation concentrates on algorithmic points, with an emphasis on attention-grabbing visualization issues of stylish ideas. a lot cognizance is paid to a uniform type of writing and presentation, constant terminology, and complementary insurance of the correct concerns in the course of the 10 chapters.

This instructional is ultimate as an advent for newbies to graph drawing. Ambitioned practitioners and researchers energetic within the zone will locate it a important resource of reference and information.

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**Extra resources for Drawing Graphs: Methods and Models**

**Example text**

Labeling. , naming nodes and edges in the drawing. Methods for labeling are discussed in Chapter 10. These aesthetics and eﬃciency criteria stand in contrast to more intuitive criteria concerning the semantics and intended meanings of graphs. 5 shows, the semantics and the structure of a graph can give very diﬀerent hints for the layout. 6. It can be speculated that the lack of layout algorithms respecting the semantics of graphs and therefore being more capable of creating a drawing that is informative as well as “favourable to the eye” lies in the nature of the problem.

Since we have to perform a planarity test for each edge of the graph and such a test can be implemented in linear time, this algorithm has 2. Drawing Planar Graphs 31 a running time of O(n · m) where n is the number of vertices in the graph and m the number of edges. Di Battista and Tamassia developed a data structure called SPQR-tree, which can be used for decomposing a planar 2-connected graph into its 3connected components and for fast online planarity testing (Di Battista and Tamassia, 1989; Di Battista and Tamassia, 1990; Di Battista and Tamassia, 1996).

The algorithm needs a depth ﬁrst search tree G = (V, T, B), where V is the set of DFS numbers of the vertices in G, T is the set of tree edges of the depth ﬁrst search tree and B the set of back edges (for DFS trees, see Mehlhorn (1984)). We assume that G is 2-connected (this is not a restriction, because a graph is planar if and only if all its 2-connected components are planar). Let C be a spine cycle of G, which is a cycle consisting of a path of tree edges starting at the root (vertex 1) of the DFS tree followed by a single back edge back to the root vertex.