Journal of Graph Algorithms and Applications More Flexible Radial Layout

We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy networks, when structural centrality is mapped to geometric centrality, or when the primary intention of the layout is the display of the vicinity of a distinguished node. We extend stress majorization by a weighting scheme which imposes radial constraints on the layout but also tries to preserve as much information about the graph structure as possible.

[1]  Ulrik Brandes,et al.  Crossing Reduction in Circular Layouts , 2004, WG.

[2]  Graham J. Wills,et al.  NicheWorks - Interactive Visualization of Very Large Graphs , 1997, GD.

[3]  Marie-Jose Carpano,et al.  Automatic Display of Hierarchized Graphs for Computer-Aided Decision Analysis , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Ulrik Brandes,et al.  Eigensolver Methods for Progressive Multidimensional Scaling of Large Data , 2006, GD.

[5]  Kim Marriott,et al.  Topology Preserving Constrained Graph Layout , 2009, GD.

[6]  Victor E. McGee,et al.  THE MULTIDIMENSIONAL ANALYSIS OF ‘ELASTIC’ DISTANCES , 1966 .

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

[8]  J. Leeuw Applications of Convex Analysis to Multidimensional Scaling , 2000 .

[9]  Ulrik Brandes,et al.  An Experimental Study on Distance-Based Graph Drawing , 2009, GD.

[10]  Mary L. Northway,et al.  A Method for Depicting Social Relationships Obtained by Sociometric Testing , 1940 .

[11]  Yifan Hu,et al.  Efficient Node Overlap Removal Using a Proximity Stress Model , 2009, GD.

[12]  Kim Marriott,et al.  Constrained graph layout by stress majorization and gradient projection , 2009, Discret. Math..

[13]  I. Borg,et al.  A model and algorithm for multidimensional scaling with external constraints on the distances , 1980 .

[14]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[15]  Willem J. Heiser,et al.  Constrained Multidimensional Scaling, Including Confirmation , 1983 .

[16]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[17]  Yehuda Koren,et al.  Graph Drawing by Stress Majorization , 2004, GD.

[18]  Ulrik Brandes,et al.  Communicating Centrality in Policy Network Drawings , 1999, IEEE Trans. Vis. Comput. Graph..

[19]  Christian Bachmaier,et al.  A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information , 2007, IEEE Transactions on Visualization and Computer Graphics.

[20]  Yehuda Koren,et al.  The Binary Stress Model for Graph Drawing , 2009, GD.

[21]  J. Leeuw Convergence of the majorization method for multidimensional scaling , 1988 .

[22]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Marti A. Hearst,et al.  Animated exploration of dynamic graphs with radial layout , 2001, IEEE Symposium on Information Visualization, 2001. INFOVIS 2001..

[24]  Trevor F. Cox,et al.  Metric multidimensional scaling , 2000 .

[25]  P. Groenen,et al.  Modern multidimensional scaling , 1996 .

[26]  Seok-Hee Hong,et al.  The Metro Map Layout Problem , 2004, InVis.au.

[27]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .