Visualization of clustered directed acyclic graphs with node interleaving

Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. An important subset of graphs is directed acyclic graphs (DAGs). E-Spring algorithm, extended from the popular spring embedder model, eliminates node overlaps in clustered DAGs by modeling nodes as charged particles whose repulsion is controlled by edges modeled as springs. The drawing process needs to reach a stable state when the average distances of separation between nodes are near optimal. This paper presents an enhancement to E-Spring to introduce a stopping condition, which reduces equilibrium distances between nodes and therefore results in a significantly reduced area for DAG visualization. It imposes an upper bound on the repulsive forces between nodes based on graph geometry. The algorithm employs node interleaving to eliminate any residual node overlaps. These new techniques have been validated by visualizing eBay buyer-seller relationships and resulted in overall area reductions in the range of 45% to 79%.

[1]  G. W. Furnas,et al.  Generalized fisheye views , 1986, CHI '86.

[2]  Peter Eades,et al.  Multilevel Visualization of Clustered Graphs , 1996, GD.

[3]  Peter Eades,et al.  A Heuristic for Graph Drawing , 1984 .

[4]  Peter Rodgers,et al.  Applying graphical design techniques to graph visualisation , 2005, Ninth International Conference on Information Visualisation (IV'05).

[5]  C. Yeh,et al.  Technique to minimise area overhead for delay-driven clustering , 1995 .

[6]  Wei Lai,et al.  Layout adjustment and boundary detection for a diagram , 2001, Proceedings. Computer Graphics International 2001.

[7]  Peter Eades,et al.  User Hints for Map Labelling , 2003, ACSC.

[8]  Michael Kaufmann,et al.  Drawing graphs: methods and models , 2001 .

[9]  Junbin Gao,et al.  A new algorithm for removing node overlapping in graph visualization , 2007, Inf. Sci..

[10]  Kevin B. Korb,et al.  Bayesian Artificial Intelligence , 2004, Computer science and data analysis series.

[11]  Kang Zhang,et al.  Social Network Analysis of Online Marketplaces , 2007 .

[12]  Peter Eades,et al.  Using Spring Algorithms to Remove Node Overlapping , 2005, APVIS.

[13]  Ivan Herman,et al.  Density functions for visual attributes and effective partitioning in graph visualization , 2000, IEEE Symposium on Information Visualization 2000. INFOVIS 2000. Proceedings.

[14]  Peter Eades,et al.  FADE: Graph Drawing, Clustering, and Visual Abstraction , 2000, GD.

[15]  Peter Eades,et al.  Navigating software architectures with constant visual complexity , 2005, 2005 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC'05).

[16]  Ivan Herman,et al.  Graph Visualization and Navigation in Information Visualization: A Survey , 2000, IEEE Trans. Vis. Comput. Graph..

[17]  Kang Zhang,et al.  Visualization of Clustered Directed Acyclic Graphs without Node Overlapping , 2008, 2008 12th International Conference Information Visualisation.

[18]  Xuemin Lin,et al.  Spring algorithms and symmetry , 1997, Theor. Comput. Sci..

[19]  Kozo Sugiyama,et al.  Layout Adjustment and the Mental Map , 1995, J. Vis. Lang. Comput..

[20]  Michael Stepp,et al.  Growing fat graphs , 2002, SCG '02.

[21]  Robert F. Cohen,et al.  Validating Graph Drawing Aesthetics , 1995, GD.

[22]  Satoru Kawai,et al.  An Algorithm for Drawing General Undirected Graphs , 1989, Inf. Process. Lett..

[23]  Mathias Lux,et al.  Emir : Semantics in Multimedia Retrieval and Annotation , 2004 .