## Simultaneous graph drawing: Layout algorithms and visualization schemes (2003)

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Venue: | In 11th Symposium on Graph Drawing (GD |

Citations: | 22 - 6 self |

### BibTeX

@INPROCEEDINGS{Erten03simultaneousgraph,

author = {C. Erten and S. G. Kobourov and V. Le and A. Navabi},

title = {Simultaneous graph drawing: Layout algorithms and visualization schemes},

booktitle = {In 11th Symposium on Graph Drawing (GD},

year = {2003},

pages = {437--449}

}

### Years of Citing Articles

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### Abstract

Abstract. In this paper we consider the problem of drawing and displaying a series of related graphs, i.e., graphs that share all, or parts of the same vertex set. We designed and implemented three different algorithms for simultaneous graphs drawing and three different visualization schemes. The algorithms are based on a modification of the force-directed algorithm that allows us to take into account vertex weights and edge weights in order to achieve mental map preservation while obtaining individually readable drawings. The implementation is in Java and the system can be downloaded at

### Citations

527 | A heuristic for graph drawing
- Eades
- 1984
(Show Context)
Citation Context ...n top of each other in the order that the graphs appear in the sequence. 3. In the split view model each graph is displayed in its own drawing window. 2 Previous Work Classical force-directed methods =-=[9, 11, 18]-=- for graph drawing use a random initial embedding of the graph and treat the graph as a system of interacting physical objects. Force-directed layout algorithms typically employ an energy function tha... |

453 | Graph Drawing by Force-directed Placement
- Fruchterman, Reingold
- 1991
(Show Context)
Citation Context ...itial random placement of the nodes inside a drawing window frame of prespecified size. The graph is then treated as a system of interacting physical objects, based on attractive and repulsive forces =-=[10]-=- or graph distances [15]. Force-directed layout algorithms employ an energy function that characterizessC. Erten et al., Simultaneous Graph Drawing, JGAA, 9(1) 165–182 (2005) 167 Figure 1: Two snapsho... |

359 | Graph visualization and navigation in information visualization: A survey
- Herman, Melançon, et al.
- 2000
(Show Context)
Citation Context ...mic graph drawing the goal is to maintain a nice layout of a graph that is modified via operations such as insert/delete edge and insert/delete node. Techniques based on static layouts have been used =-=[4, 13, 19]-=-. North [17] studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the force-directed model to dynamic graphs using a Bayesian framework [3]. Diehl and Görg [6]... |

152 |
Layout adjustment and the mental map
- Misue, Eades, et al.
- 1995
(Show Context)
Citation Context ...8]. Preservation of the mental map can be achieved by ensuring that common substructures (nodes, edges, subgraphs etc.) that appear in consecutive graphs in the series, are drawn in a similar fashion =-=[16]-=-. These two criteria are often contradictory. If we individually layout each graph, without regard to other graphs in the series, we may optimize readability at the expense of mental map preservation.... |

136 |
Which aesthetic has the greatest effect on human understanding
- Purchase
- 1997
(Show Context)
Citation Context ...l map preservation in the series of drawings. The readability of individual drawings depends on aesthetic criteria such as display of symmetries, uniform edge lengths, and minimal number of crossings =-=[18]-=-. Preservation of the mental map can be achieved by ensuring that common substructures (nodes, edges, subgraphs etc.) that appear in consecutive graphs in the series, are drawn in a similar fashion [1... |

87 | A system for graph-based visualization of the evolution of software
- Collberg, Kobourov, et al.
- 2003
(Show Context)
Citation Context ..., 10] imply that simultaneous embeddings exist only for special cases and relaxations of the problem (such as the one we address in this paper) should be considered. Along these lines, Collberg et al =-=[7]-=- describe a graph-based system for visualization of software evolution, which uses a modification of our algorithm for visualization of large graphs [12], while preserving the mental map by fixing the... |

84 | Animated exploration of dynamic graphs with radial layout
- Yee, Fisher, et al.
- 2001
(Show Context)
Citation Context ...mic graph drawing the goal is to maintain a nice layout of a graph that is modified via operations such as insert/delete edge and insert/delete node. Techniques based on static layouts have been used =-=[4, 13, 19]-=-. North [17] studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the force-directed model to dynamic graphs using a Bayesian framework [3]. Diehl and Görg [6]... |

55 | Visual unrolling of network evolution and the analysis of dynamic discourse
- Brandes, Corman
- 2002
(Show Context)
Citation Context ...graphs in a sequence to create smoother transitions. Special classes of graphs such as trees, series-parallel graphs and st-graphs have also been studied in dynamic models [6, 19]. Brandes and Corman =-=[2]-=- present a system for visualizing network evolution in which each modification is shown in a separate layer of 3D representation with vertices common to two layers represented as columns connecting th... |

55 | D.: A bayesian paradigm for dynamic graph layout
- Brandes, Wagner
- 1997
(Show Context)
Citation Context ...ve been used [4, 16, 21]. North [20] studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the forcedirected model to dynamic graphs using a Bayesian framework =-=[3]-=-. Diehl and Görg [8] 3sconsider graphs in a sequence to create smoother transitions. Special classes of graphs such as trees, series-parallel graphs and st-graphs have also been studied in dynamic mod... |

43 | C.: Incremental layout in DynaDAG
- North
- 1995
(Show Context)
Citation Context ...he goal is to maintain a nice layout of a graph that is modified via operations such as insert/delete edge and insert/delete node. Techniques based on static layouts have been used [4, 13, 19]. North =-=[17]-=- studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the force-directed model to dynamic graphs using a Bayesian framework [3]. Diehl and Görg [6] consider gr... |

42 | GraphAEL: Graph animations with evolving layouts
- Erten, Harding, et al.
- 2004
(Show Context)
Citation Context ...graphs obtained from a file system (also shown using the aggregate layout algorithm and aggregate view in Fig. 1). Finally, we show several graphs obtained from the Graph Drawing Proceedings database =-=[9]-=-. In Fig. 13 we show a piece of the Graph Drawing topic graph. A topic graph for a given time interval has as nodes the dominant keywords/phrases used in publications during that period. The edges con... |

35 | GRIP: Graph dRawing with Intelligent Placement
- Gajer, Kobourov
- 2000
(Show Context)
Citation Context ...ced in a similar manner, using three previously placed nodes. Once all the nodes have been placed, several iterations of the force-directed method are applied. This approach is described in detail in =-=[11]-=-. At the conclusion of this stage, we have “good” layouts for each graph when they are drawn independently. As a result we obtain two different point-sets, P1 and P2 specifying the locations of the no... |

32 |
Dynamic graph drawing
- Branke
- 1999
(Show Context)
Citation Context ...c graph drawing the goal is to maintain a nice layout of a graph that is modified via operations such as insert/delete edge and insert/delete vertex. Techniques based on static layouts have been used =-=[4, 16, 21]-=-. North [20] studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the forcedirected model to dynamic graphs using a Bayesian framework [3]. Diehl and Görg [8] ... |

30 | Drawing graphs with non-uniform vertices
- Harel, Koren
- 2002
(Show Context)
Citation Context ...indow frame, C is a constant determining how the nodes fill the frame, and n is the total number of nodes. Several variations of force-directed methods for edge-weighted graphs have been proposed. In =-=[8, 12]-=- edge-weighted graphs are drawn so that the length of edges is proportional to their weights. Similarly, layouts for node-weighted graphs have also been considered in the context of focus-nodes that a... |

27 |
Graphs, They Are Changing
- Diehl, Görg
- 2002
(Show Context)
Citation Context ... 21]. North [20] studies the incremental graph drawing problem in the DynaDAG system. Brandes and Wagner adapt the forcedirected model to dynamic graphs using a Bayesian framework [3]. Diehl and Görg =-=[8]-=- 3sconsider graphs in a sequence to create smoother transitions. Special classes of graphs such as trees, series-parallel graphs and st-graphs have also been studied in dynamic models [6, 19]. Brandes... |

26 | Drawing on physical analogies
- Brandes
- 2001
(Show Context)
Citation Context ... in all graphs and draw common edges the same way, we are optimizing the mental map preservation but the individual layouts may be far from readable. 1.1 Related Work Classical force-directed methods =-=[1]-=- for graph drawing typically begin with an initial random placement of the nodes inside a drawing window frame of prespecified size. The graph is then treated as a system of interacting physical objec... |

22 |
On-line animated visualization of huge graphs using a modified spring algorithm
- Huang, Eades, et al.
- 1998
(Show Context)
Citation Context ...node-weighted graphs have also been considered in the context of focus-nodes that apply repulsive force proportional to their weight, so that the neighborhoods of such nodes will not be too cluttered =-=[14]-=-. In dynamic graph drawing the goal is to maintain a nice layout of a graph that is modified via operations such as insert/delete edge and insert/delete node. Techniques based on static layouts have b... |

17 |
Automatic display of network structures for human understanding
- Kamada, Kawai
- 1988
(Show Context)
Citation Context ...f the nodes inside a drawing window frame of prespecified size. The graph is then treated as a system of interacting physical objects, based on attractive and repulsive forces [10] or graph distances =-=[15]-=-. Force-directed layout algorithms employ an energy function that characterizessC. Erten et al., Simultaneous Graph Drawing, JGAA, 9(1) 165–182 (2005) 167 Figure 1: Two snapshots of a file structure r... |

15 |
On simultaneous graph embedding
- Brass, Duncan, et al.
- 2003
(Show Context)
Citation Context ...blem that asks whether there exist locations for the vertices of two different planar graphs such that each of the graphs can be drawn with straight lines and no crossings. Recent theoretical results =-=[5, 10]-=- imply that simultaneous embeddings exist only for special cases and relaxations of the problem (such as the one we address in this paper) should be considered. Along these lines, Collberg et al [7] d... |

15 |
Dynamic graph drawing: Trees, series–parallel digraphs, and planar st-digraphs
- Cohen, Battista, et al.
- 1995
(Show Context)
Citation Context ...ehl and Görg [8] 3sconsider graphs in a sequence to create smoother transitions. Special classes of graphs such as trees, series-parallel graphs and st-graphs have also been studied in dynamic models =-=[6, 19]-=-. Brandes and Corman [2] present a system for visualizing network evolution in which each modification is shown in a separate layer of 3D representation with vertices common to two layers represented ... |

14 | Simultaneous embedding of a planar graph and its dual on the grid
- Erten, Kobourov
(Show Context)
Citation Context ...blem that asks whether there exist locations for the vertices of two different planar graphs such that each of the graphs can be drawn with straight lines and no crossings. Recent theoretical results =-=[5, 10]-=- imply that simultaneous embeddings exist only for special cases and relaxations of the problem (such as the one we address in this paper) should be considered. Along these lines, Collberg et al [7] d... |

11 | Visualising a Fund Manager Flow Graph with Columns and Worms
- Dwyer, Eades
- 2002
(Show Context)
Citation Context ...ers represented as columns connecting the layers. Thus, mental map preservation is achieved by precomputing good locations for the nodes and fixing the position throughout the layers. Dwyer and Eades =-=[7]-=- describe a method for visualizing time dependent flow in a network of objects by representing time as the third dimension, using columns of varying width. Along these lines, Collberg et al [5] descri... |

1 |
de Mendonça Neto. Vertex splitting and tensionfree layout
- Eades, X
- 1996
(Show Context)
Citation Context ...indow frame, C is a constant determining how the nodes fill the frame, and n is the total number of nodes. Several variations of force-directed methods for edge-weighted graphs have been proposed. In =-=[8, 12]-=- edge-weighted graphs are drawn so that the length of edges is proportional to their weights. Similarly, layouts for node-weighted graphs have also been considered in the context of focus-nodes that a... |