Clustered graphs are graphs with recursive clustering structures over the vertices. This type of structure appears in many systems. Examples include CASE tools, management information systems, VLSI design tools, and reverse engineering systems. Existing layout algorithms represent the clustering structure as recursively nested regions in the plane. However, as the structure becomes more and more complex, two dimensional plane representations tend to be insufficient. In this paper, firstly, we describe some two dimensional plane drawing algorithms for clustered graphs; then we show how to extend two dimensional plane drawings to three dimensional multilevel drawings. We consider two conventions: straight-line convex drawings and orthogonal rectangular drawings; and we show some examples.
Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of planar straight-line representation has not been solved completely. In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.
Introduction. A graph G = (V, E) consists of a set V of vertices and a setE of edges, that is, pairs of vertices. Graphs are commonly used to model relations in computing, and many systems for manipulating graphs have recently been developed. Examples include CASE tools [55] knowledge representation systems [31], software visualization tools [54] and VLSI design systems [26]. A graph drawing algorithm reads as input a combinatorial description of a graph, and produces as output a visual representation of the graph. Such algorithms aim to produce drawings which are easy to read and easy to remember. Many graph drawing algorithms have been designed, analyzed, tested and used in visualization systems [2], [33].With increasing complexity of the information that we want to visualize, we need more structure on top of the classical graph model. Several extended graph models have been proposed [5], [26], [35], [49], [50]. In this paper we consider two such models:
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