## Drawing Planar Clustered Graphs in 2.5 Dimensions

Citations: | 1 - 1 self |

### BibTeX

@MISC{Mader_drawingplanar,

author = {Martin Mader and Seokhee Hong},

title = {Drawing Planar Clustered Graphs in 2.5 Dimensions},

year = {}

}

### OpenURL

### Abstract

Clustering techniques have proven to be useful in reducing the complexity of large networks. We present a method for drawing a clustered graph in 2.5D, given the clusters of the graph are connected in a planar way. The main contribution is to develop a weighted version of the well known 2D straight line drawing algorithm of de Fraysseix, Pach and Pollack [5] for planar graphs. This version allows for thick vertices and ensures a constraint we define as “visibility ” between connected vertices. The algorithm has been implemented and experimentally evaluated. 1

### Citations

153 |
How to draw a planar graph on a grid
- Fraysseix, Pach, et al.
- 1990
(Show Context)
Citation Context ... the clusters of the graph are connected in a planar way. The main contribution is to develop a weighted version of the well known 2D straight line drawing algorithm of de Fraysseix, Pach and Pollack =-=[5]-=- for planar graphs. This version allows for thick vertices and ensures a constraint we define as “visibility” between connected vertices. The algorithm has been implemented and experimentally evaluate... |

76 |
Planar Graphs: Theory and Algorithms
- Nishizeki, Chiba
- 1988
(Show Context)
Citation Context ...f planar graph drawing there are basically two different approaches to obtain a standard straight-line representation of planar graphs [3, 9, 11]: • Convex representations (Tutte [13], Convex drawing =-=[10]-=-), and • Methods based on a canonical ordering (Shift method [5], Barycenter method [12]). We present a weighted version of the shift method of deFraysseix, Pach, Pollack [5]. Given a maximally planar... |

64 |
Drawing Graphs: Methods and Models
- Kaufmann, Wagner
- 1999
(Show Context)
Citation Context ...ining the visibility constraint. 1.2 Previous work In the field of planar graph drawing there are basically two different approaches to obtain a standard straight-line representation of planar graphs =-=[3, 9, 11]-=-: • Convex representations (Tutte [13], Convex drawing [10]), and • Methods based on a canonical ordering (Shift method [5], Barycenter method [12]). We present a weighted version of the shift method ... |

37 | A linear-time algorithm for drawing a planar graph on a grid
- Chrobak, Payne
- 1995
(Show Context)
Citation Context ...Pollack [5]. Given a maximally planar graph, this algorithm calculates coordinates for each vertex on an 2D integer grid with a quadratic area bound. Chrobak and Payne presented a linear time variant =-=[4]-=-, which uses only basic data structures and is easy to implement. Harel and Sardas provide a version for biconnected graphs [7]. Our approach is closely related to another weighted version of this alg... |

14 | GEOMI: Geometry for maximum insight
- Ahmed, Dwyer, et al.
- 2005
(Show Context)
Citation Context ...ection, we present the algorithm for step 2b of the general framework. Section 3 discusses some experimental results obtained with an implementation of the algorithm in the visual analysis tool GEOMI =-=[1]-=-. We conclude in section 4 and give an outlook on open problems. 22 2D Drawing of the weighted planar supergraph 2.1 Definitions Let G = (V, E) be a triangulated planar graph with n = |V | and m = |E... |

13 | An Algorithm for Straight-Line Drawing of Planar Graphs
- Harel, Sardas
- 1995
(Show Context)
Citation Context ... quadratic area bound. Chrobak and Payne presented a linear time variant [4], which uses only basic data structures and is easy to implement. Harel and Sardas provide a version for biconnected graphs =-=[7]-=-. Our approach is closely related to another weighted version of this algorithm by Barequet, Goodrich, Riley [2], who allow for thick vertices and edges in order to visualize traffic volumes on edges ... |

9 | C.: Drawing planar graphs with large vertices and thick edges
- Barequet, Goodrich, et al.
- 2004
(Show Context)
Citation Context ...res and is easy to implement. Harel and Sardas provide a version for biconnected graphs [7]. Our approach is closely related to another weighted version of this algorithm by Barequet, Goodrich, Riley =-=[2]-=-, who allow for thick vertices and edges in order to visualize traffic volumes on edges in a network. Though the main idea is similar, there are differences in the conditions, as in our case we have i... |

4 |
Graph embedding with minimum depth and maximum external face
- Gutwenger, Mutzel
- 2004
(Show Context)
Citation Context ...r symmetry. In step 2a one could try to optimize certain measures like depth or size of the external face w.r.t. the given vertex/edge weights to improve the final aesthetic appearance of the drawing =-=[6]-=-. Clearly, this is dependent on the drawing algorithm used in step 2b. Since in this step space is assigned for the later insertion of the single clusters, the main focus here is to ensure that no cro... |

4 | Drawings Clustered Graphs in Three Dimensions
- Ho, Hong
- 2006
(Show Context)
Citation Context ...nt clustering algorithms, and many real-world networks have an inherent underlying clustered graph topology. Recently Ho and Hong presented a framework for drawing clustered graph in three dimensions =-=[8]-=-, given the connectivity between the single clusters forms a tree structure. In this paper we present a 2.5D visualization based on the same framework, where the abstract graph of clusters, the “super... |