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Geometry-Based Edge Clustering for Graph Visualization
November/December 2008 (vol. 14 no. 6)
pp. 1277-1284
Weiwei Cui, the Hong Kong University of Science and Technology
Hong Zhou, the Hong Kong University of Science and Technology
Huamin Qu, the Hong Kong University of Science and Technology
Pak Chung Wong, Pacific Northwest National Laboratory
Xiaoming Li, Peking University
Graphs have been widely used to model relationships among data. For large graphs, excessive edge crossings make the display visually cluttered and thus difficult to explore. In this paper, we propose a novel geometry-based edge-clustering framework that can group edges into bundles to reduce the overall edge crossings. Our method uses a control mesh to guide the edge-clustering process; edge bundles can be formed by forcing all edges to pass through some control points on the mesh. The control mesh can be generated at different levels of detail either manually or automatically based on underlying graph patterns. Users can further interact with the edge-clustering results through several advanced visualization techniques such as color and opacity enhancement. Compared with other edge-clustering methods, our approach is intuitive, flexible, and efficient. The experiments on some large graphs demonstrate the effectiveness of our method.

[1] D. Archambault, T. Munzner, and D. Auber, TopoLayout: Multilevel graph layout by topological features. IEEE Transactions on Visualization and Computer Graphics, 13 (2): 305–317, 2007.
[2] G. D. Battista, P. Eades, R. Tamassia, and I. G. Tollis, Graph Drawing; Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
[3] L. P. Chew, Constrained Delaunay triangulations. In Proceed. of the Symposium on Computational Geometry, pages 215–222, 1987.
[4] R. Davidson and D. Harel, Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics (TOG), 15 (4): 301–331, 1996.
[5] M. Dickerson, D. Eppstein, M. T. Goodrich, and J. Y. Meng, Confluent drawings: Visualizing non-planar diagrams in a planar way. J. Graph Algorithms Appl., 9 (1): 31–52, 2005.
[6] R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis. Wiley, 1973.
[7] G. Ellis and A. Dix, A taxonomy of clutter reduction for information visualisation. IEEE Transactions on Visualization and Computer Graphics, 13 (6): 1216–1223, 2007.
[8] A. Frick, A. Ludwig, and H. Mehldau, A Fast Adaptive Layout Algorithm for Undirected Graphs. Proceedings of the DIMACS International Workshop on Graph Drawing, pages 388–403, 1994.
[9] Y. Frishman and A. Tal, Multi-level graph layout on the GPU. IEEE Transactions on Visualization and Computer Graphics, 13 (6): 1310–1319, 2007.
[10] E. Gansner, Y. Koren, and S. North, Topological fisheye views for visualizing large graphs. In Proc. of the IEEE Symp. on Information Visualization, pages 175–182, 2004.
[11] E. R. Gansner and Y. Koren, Improved circular layouts. In Proceed. of Symposium on Graph Drawing, pages 386–398, 2006.
[12] D. Holten, Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data. IEEE Transactions on Visualization and Computer Graphics, 12 (5): 741–748, 2006.
[13] P. Hui, M. Pelsmajer, M. Schaefer, and D. Stefankovic, Train Tracks and Confluent Drawings. Procced. of Symposium on Graph Drawing, pages 465–479, 2004.
[14] J. Johansson, P. Ljung, M. Jern, and M. Cooper, Revealing structure within clustered parallel coordinates displays. In Proc. of IEEE Symp. on Information Visualization, pages 125–132, 2005.
[15] M. Kaufmann and D. Wagner, Drawing Graphs: Methods and Models. Springer, 2001.
[16] Y. Koren, L. Carmel, and D. Harel, Drawing huge graphs by algebraic multigrid optimization. SIAM Multiscale Modeling and Simulation, 1 (4): 645–673, 2003.
[17] A. Noack, An energy model for visual graph clustering. In Proceed. of Symposium on Graph Drawingg, pages 425–436, 2003.
[18] D. Phan, L. Xiao, R. Yeh, P. Hanrahan, and T. Winograd, Flow map layout. IEEE Symposium on Information Visualization 2005, pages 219–224, 2005.
[19] H. Qu, H. Zhou, and Y. Wu, Controllable and progressive edge clustering for large networks. In Proceed. of Symposium on Graph Drawing, pages 399–404, 2006.
[20] F. van Ham and J. J. van Wijk, Interactive visualization of small world graphs. IEEE Symposium on Information Visualization 2004, pages 199–206, 2004.
[21] N. Wong, M. Carpendale, and S. Greenberg, Edgelens: An interactive method for managing edge congestion in graphs. IEEE Symposium on Information Visualization 2003, pages 51–58, 2003.
[22] N. Wong and S. Carpendale, Interactive poster: Using edge plucking for interactive graph exploration. Poster in the IEEE Symposium on Information Visualization, 2005.
[23] P. C. Wong, H. Foote, G. C. Jr., P. Mackey, and K. Perrine, Graph signatures for visual analytics. IEEE Transactions on Visualization and Computer Graphics, 12 (6): 1399–1413, 2006.

Index Terms:
Index Terms—Graph visualization, visual clutter, mesh, edge clustering
Citation:
Weiwei Cui, Hong Zhou, Huamin Qu, Pak Chung Wong, Xiaoming Li, "Geometry-Based Edge Clustering for Graph Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 6, pp. 1277-1284, Nov.-Dec. 2008, doi:10.1109/TVCG.2008.135
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