A Simplification Algorithm for Visualizing the Structure of Complex Graphs

Complex graphs, ones containing thousands of nodes of high degree, are difficult to visualize. Displaying all of the nodes and edges of these graphs can create an incomprehensible cluttered output. This paper presents a simplification algorithm that may be applied to a complex graph in order to produce a controlled thinning of the graph. Using importance metrics, the simplification process removes nodes from the graph, leaving the central structure for visualization and evaluation. The simplification algorithm consists of two steps, calculation of the importance metrics and pruning. Several metrics based on various topological graph properties are described. The metrics are then used in a pruning process to simplify the graph. Nodes, along with their corresponding edges, are removed from the graph, while maintaining the graph's overall connectivity. This simplified graph provides a cleaner, more meaningful visual representation of the graph's structure; thus aiding the analysis of the graph's underlying data.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  Ayellet Tal,et al.  Multi-Level Graph Layout on the GPU , 2007, IEEE Transactions on Visualization and Computer Graphics.

[3]  Dibakar Sen,et al.  Graph based topological analysis of tessellated surfaces , 2003, SM '03.

[4]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Stephen Curial,et al.  Effectively visualizing large networks through sampling , 2005, VIS 05. IEEE Visualization, 2005..

[6]  Stefano Rizzi,et al.  A genetic approach to hierarchical clustering of Euclidean graphs , 1998, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[7]  Edwin R. Hancock,et al.  Spectral Simplification of Graphs , 2004, ECCV.

[8]  Ming-Yang Kao,et al.  Simple and Efficient Graph Compression Schemes for Dense and Complement Graphs , 1998, J. Comb. Optim..

[9]  Sugih Jamin,et al.  Inet-3.0: Internet Topology Generator , 2002 .

[10]  Anna C. Gilbert,et al.  Compressing Network Graphs , 2004 .

[11]  Rajeev Motwani,et al.  Clique partitions, graph compression and speeding-up algorithms , 1991, STOC '91.

[12]  Steven P. Weber,et al.  Cross-layer multicommodity capacity expansion on ad hoc wireless networks of cognitive radios , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[13]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[14]  Cigdem Demir,et al.  Augmented cell-graphs for automated cancer diagnosis , 2005, ECCB/JBI.

[15]  Mary P. Harper,et al.  The effect of pruning and compression on graphical representations of the output of a speech recognizer , 2003, Comput. Speech Lang..

[16]  Edwin R. Hancock,et al.  Graph simplification and matching using commute times , 2007, Pattern Recognit..

[17]  Torsten Suel,et al.  Compressing the graph structure of the Web , 2001, Proceedings DCC 2001. Data Compression Conference.

[18]  Chaomei Chen,et al.  CiteSpace II: Detecting and visualizing emerging trends and transient patterns in scientific literature , 2006, J. Assoc. Inf. Sci. Technol..