## Multilevel Visualization of Clustered Graphs (1997)

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Citations: | 87 - 2 self |

### BibTeX

@INPROCEEDINGS{Eades97multilevelvisualization,

author = {Peter Eades and Qingwen Feng},

title = {Multilevel Visualization of Clustered Graphs},

booktitle = {},

year = {1997},

pages = {101--112},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 ...

### Citations

572 | On Visual Formalisms
- Harel
- 1988
(Show Context)
Citation Context ...over the vertices are called clustered graphs (see Fig. 1). This type of structure appears in many systems. Examples include CASE tools [16], management information systems [8], and VLSI design tools =-=[7]-=-. In two dimensional representations, the clustering structure is represented by region inclusions, i.e. a cluster is represented by a simple region that contains the drawing of all the vertices which... |

391 | How to draw a graph
- Tutte
- 1963
(Show Context)
Citation Context ...nts, regions for clusters are drawn as convex polygons. We use two approaches for such drawings. An approach based on Tutte's algorithm. This approach from [6] applies a well known algorithm of Tutte =-=[15]-=-, which creates a straight-line planar drawing of a triconnected planar graph G such that every face is a convex polygon. To apply Tutte's algorithm, we construct a skeleton \Gamma( ) for each cluster... |

97 | Automatic Graph Drawing and Readability of Diagrams
- Tamassia, Battista, et al.
- 1988
(Show Context)
Citation Context ...ng the algorithm in [2], we obtain a visibility representation of the graph. Finally, we construct an orthogonal rectangular drawing from the visibility drawing using some local operations similar to =-=[14]-=-. 4 Multilevel Drawings In this section we discuss methods of producing multilevel drawings of clustered graphs. We take the two dimensional plane drawings produced by the algorithms described in the ... |

73 |
Kazuo Misue. Visualization of structural information: automatic drawing of compound digraphs
- Sugiyama
- 1991
(Show Context)
Citation Context ...esented by a simple region that contains the drawing of all the vertices which belong to that cluster (see Fig. 2). For such drawings, some heuristic methods have been developed by Sugiyama and Misue =-=[13, 10]-=-, by North [11], and by Madden et al. [12, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular dra... |

64 |
Computing an st-numbering
- EVEN, TARJAN
- 1976
(Show Context)
Citation Context ...her-numbered vertex. Vertices s and t are called the source and the sink respectively. Such a numbering is an st numbering for G. An st numbering of a biconnected graph can be computed in linear time =-=[5]-=-. 2 A planar st-graph [1] is a planar directed graph with one source s and one sink t; and both source and sink above can be embedded on the boundary of the same face, say the external face. side of a... |

60 |
Algorithms for plane representations of acyclic digraphs
- DiBattista, Tamassia
- 1988
(Show Context)
Citation Context ...ices s and t are called the source and the sink respectively. Such a numbering is an st numbering for G. An st numbering of a biconnected graph can be computed in linear time [5]. 2 A planar st-graph =-=[1]-=- is a planar directed graph with one source s and one sink t; and both source and sink above can be embedded on the boundary of the same face, say the external face. side of a rectangle. We also add s... |

60 | Straight-line drawing algorithms for hierarchical graphs and clustered graphs
- Eades, Feng, et al.
- 1996
(Show Context)
Citation Context ...methods have been developed by Sugiyama and Misue [13, 10], by North [11], and by Madden et al. [12, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin =-=[6, 4]-=-. An algorithm for planar orthogonal rectangular drawings is presented by Eades and Feng in [3]. However, as the clustering structure becomes more and more complex, two dimensional representations ten... |

47 |
Planarity for clustered graphs
- Feng, Cohen, et al.
- 1995
(Show Context)
Citation Context ...methods have been developed by Sugiyama and Misue [13, 10], by North [11], and by Madden et al. [12, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin =-=[6, 4]-=-. An algorithm for planar orthogonal rectangular drawings is presented by Eades and Feng in [3]. However, as the clustering structure becomes more and more complex, two dimensional representations ten... |

29 |
The state of the art of visual languages for visualization
- Williams, Rasure, et al.
- 1992
(Show Context)
Citation Context ...ssical graph model. Graphs with recursive clustering structures over the vertices are called clustered graphs (see Fig. 1). This type of structure appears in many systems. Examples include CASE tools =-=[16]-=-, management information systems [8], and VLSI design tools [7]. In two dimensional representations, the clustering structure is represented by region inclusions, i.e. a cluster is represented by a si... |

13 |
Tollis, Constrained visibility representations of graphs
- Battista, Tamassia, et al.
- 1992
(Show Context)
Citation Context ...esentation. Here again, we compute a c-st numbering of G. Then we apply a direction for each edge of G according to the c-st numbering, and therefore obtain a planar st-graph. We use the technique in =-=[2]-=- of producing visibility representations of planar st-graphs. To obtain a rectangle for each cluster , we add 4 dummy vertices, each represents one 1 Given any edge (s; t) in a biconnected graph G wit... |

13 |
Drawing ranked digraphs with recursive clusters, in
- North
- 1993
(Show Context)
Citation Context ... region that contains the drawing of all the vertices which belong to that cluster (see Fig. 2). For such drawings, some heuristic methods have been developed by Sugiyama and Misue [13, 10], by North =-=[11]-=-, and by Madden et al. [12, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular drawings is presen... |

11 |
The KJ method - A scientific approach to problem solving
- Kawakita
- 1975
(Show Context)
Citation Context ...sive clustering structures over the vertices are called clustered graphs (see Fig. 1). This type of structure appears in many systems. Examples include CASE tools [16], management information systems =-=[8]-=-, and VLSI design tools [7]. In two dimensional representations, the clustering structure is represented by region inclusions, i.e. a cluster is represented by a simple region that contains the drawin... |

9 |
An Overview of Diagram Based Idea Organizer: D-Abductor
- Misue, Sugiyama
- 1993
(Show Context)
Citation Context ...esented by a simple region that contains the drawing of all the vertices which belong to that cluster (see Fig. 2). For such drawings, some heuristic methods have been developed by Sugiyama and Misue =-=[13, 10]-=-, by North [11], and by Madden et al. [12, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular dra... |

4 | Orthogonal grid drawing of clustered graphs
- Eades, Feng
- 1996
(Show Context)
Citation Context ...2, 9]. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular drawings is presented by Eades and Feng in =-=[3]-=-. However, as the clustering structure becomes more and more complex, two dimensional representations tend to be insufficient. A common strategy for visualizing large graphs with recursive clusterings... |

4 |
Portable graph layout and editing
- Madden, Madden, et al.
- 1027
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Citation Context ...contains the drawing of all the vertices which belong to that cluster. For such representation, some heuristic methods have been developed by Sugiyama and Misue [6], by North [5], and by Madden et al =-=[4]-=-. Methods for planar straightline convex layout have been developed by Eades, Feng and Lin [3, 2]. An approach for planar orthogonal rectangular representation has been developed by Eades and Feng [1]... |

3 |
Graph layout toolkit. available from bmadden @TomSawyer.COM
- Software
(Show Context)
Citation Context ...rawing of all the vertices which belong to that cluster (see Fig. 2). For such drawings, some heuristic methods have been developed by Sugiyama and Misue [13, 10], by North [11], and by Madden et al. =-=[12, 9]-=-. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular drawings is presented by Eades and Feng in [3]. ... |

2 |
Portable graph layout end editing
- Madden, Madden, et al.
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Citation Context ...rawing of all the vertices which belong to that cluster (see Fig. 2). For such drawings, some heuristic methods have been developed by Sugiyama and Misue [13, 10], by North [11], and by Madden et al. =-=[12, 9]-=-. Algorithms for planar straight-line convex drawings have been developed by Eades, Feng and Lin [6, 4]. An algorithm for planar orthogonal rectangular drawings is presented by Eades and Feng in [3]. ... |