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. 1 Introduction Graph drawing algorithms are widely used in graphical user interfaces of software systems. As the amount of information that we want to visualize becomes larger, we need more structure ...

In order to realise the potential benefits of three--dimensional (3D) display of relational information, there is a need for effective 3D human--computer interface designs. Algorithms for automatically creating 3D visual representations of relational information are a significant component of these interfaces. One productive strategy for developing such algorithms has been via the graph as an intermediate representation of the relational information: the information is first expressed as a graph and then a layout algorithm is used to create a visual representation of the graph. This thesis examines some technical issues which arise when several common layout algorithms, developed originally for 2D display of graphs, are extended specifically to 3D display. Typical computer graphics display systems can only provide a limited resolution and display area. This places a limit on the size of graph which can be displayed effectively. Simplification of the graph can permit the display of lar...

The use of ternary diagrams to represent normalised call graph directions permit the succinct visualisations of object-oriented (OO) systems. Important features of such diagrams include (i) the ability to compare different object-oriented applications; and (ii) the potential ability to make value judgments about partially completed systems. Ternary diagrams also permit an overview of very large graphs. For example, we present here a visualisation of five OO applications comprising 1,643 vertices and 194,451 edges. 1 Introduction A call graph is a directed graph whose vertices represent basic data values and whose edges represent how those basic data values are passed to sub-routines. An anonymous call graph is a call graph where all the vertices have been changed to anonymous variables (e.g. class0023) and the source of the call graph is not recorded with the graph. Call graphs offer a uniform view for a variety of programming systems. For example, the dependency network within a prop...

In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs. Given a clustered graph, the C-planarity testing problem is to determine whether the clustered graph can be drawn without edge crossings, or edge-region crossings. In this paper, we present efficient algorithms for testing C-planarity and finding C-planar embeddings of clustered graphs. 1 Introduction Representing information visually, or by drawing graphs can greatly improve the effectiveness of user interfaces in many relational information systems [12, 17, 18, 5]. Developing algorithms for drawing graphs automatically and efficiently has become the interest of research for many computer scientists. Research in this area has been very active for the last decade. A recent survey citelabel13new of literature in this area inclu...

Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal-grid rectangular cluster drawings. The drawing produced by the algorithm has constant number of bends on each edge and has O(n 2 ) area, which is as good as existing results for classical graph drawings. 1 Introduction Clustered graphs are graphs with recursive clustering structures over the vertices (see Fig. 1). This type of clustering structure appears in many systems. Examples include CASE tools [19], management information systems [10], and VLSI design tools [8]. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which ...

Graphs are often used to represent relational information. As the amount of information that we want to visualize becomes larger and more complicated, classical graph model tends to be insufficient. In this paper, we introduce and show how to draw a practical and simple graph structure known as clustered graphs. We present an algorithm which produces planar, straight-line, convex drawings of clustered graphs in O(n 2:5 ) time. We also demonstrate an area lower bound and an angle upper bound for straight-line convex drawings of C-planar graphs. We show that such drawings require\Omega\Gammaq n ) area and the smallest angle is O(1=n). Our bounds are unlike the area and angle bounds of classical graph drawing conventions in which area bound is \Omega\Gamma n 2 ) and angle bounds are functions of the maximum degree of the graph. Our results indicate important tradeoffs between line straightness and area, and between region convexity and area. 1 Introduction Many systems, particular...

In this paper we present a topology viewer for the NaradaBrokering [FP02] system. The NaradaBrokering system comprises a distributed network of cooperating broker nodes organized within a logical overlay network. The topology viewer’s layout algorithm is implemented such that it augments the structure of the NaradaBrokering network. Furthermore, we believe that this approach could also be applied to similar visualization problems. Our visualization scheme extends recent work in the visualization of large hierarchies with primary focus on algorithmic and visual simplicity. Specifically, we have modified the ringed layout algorithm for placement of various NaradaBrokering components in order to achieve navigational efficiency. The scheme also helps user view information associated with nodes and links besides navigating through the network hierarchy. We have tested the topology viewer with up to ten thousand nodes and we include these performance measurements in this paper. Visualization of network topologies is a challenging problem. Networks can be thought of as graphs. A graph has two main components – a set of nodes and a set of edges (relations). Given a set of nodes and a corresponding set of edges, the basic graph drawing problem involves the calculation of the position of the nodes and the curve that needs to be drawn for each edge [HMM00]. There are number of factors which decide the quality

Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. We present an algorithm which produces such drawings with O(n 2 ) area and with at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that the bend performance of our algorithm is optimal. (Extended Abstract) 1 Introduction Clustered graphs are graphs with recursive clustering structures over the vertices (see Figure 1). This type of clustering structure appears in many systems. Examples include CASE tools [40], management information systems [19], and VLSI design tools [15]. For graphical representation, the clust...

The central topic of this thesis are criteria and tests which reveal whether a given clustered graph allows an embedding in the plane for which no edges and clusters intersect. Together with their definition in 1996, a notion of planarity was presented for clustered graphs, as well as an algorithm which tests this planarity for a given clustered graph in linear time. The algorithm however expects each cluster to be connected. For general clustered graphs, no efficient algorithm is yet known, neither is the computational complexity of the problem. This work presents algorithms which extend the class of clustered graphs for which planarity can be tested in polynomial time. A second part considers a weak form of planarity, and shows that a polynomial time test for this form also yields a polynomial time test for the classical definition. Furthermore, an attempt is made, by means of a characterization of the weak realizability problem in terms of forbidden subgraphs, to gain a similar characterization of the weak form of cluster planarity.