
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Liran Carmel, David Harel, Yehuda Koren, "Combining Hierarchy and Energy Drawing Directed Graphs," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 1, pp. 4657, JanuaryFebruary, 2004.  
BibTex  x  
@article{ 10.1109/TVCG.2004.1260757, author = {Liran Carmel and David Harel and Yehuda Koren}, title = {Combining Hierarchy and Energy Drawing Directed Graphs}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {10}, number = {1}, issn = {10772626}, year = {2004}, pages = {4657}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2004.1260757}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Combining Hierarchy and Energy Drawing Directed Graphs IS  1 SN  10772626 SP46 EP57 EPD  4657 A1  Liran Carmel, A1  David Harel, A1  Yehuda Koren, PY  2004 KW  Directed graph drawing KW  force directed layout KW  hierarchy energy KW  Fiedler vector KW  minimum linear arrangement. VL  10 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract We present an algorithm for drawing directed graphs which is based on rapidly solving a unique onedimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.
[1] U. Brandes, G. Shubina, R. Tamassia, and D. Wagner, Fast Layout Methods for Timetable Graphs Proc. Graph Drawing (GD '00), pp. 127138, 2000.
[2] R. Davidson and D. Harel, Drawing Graphs Nicely Using Simulated Annealing ACM Trans. Graphics, vol. 15, pp. 301331, 1996.
[3] G. Di Battista, P. Eades, R. Tamassia, and I.G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
[4] J. Diaz, J. Petit, and M. Serna, A Survey on Graph Layout Problems ACM Computing Surveys, vol. 34, pp. 313356, 2002.
[5] P. Eades, A Heuristic for Graph Drawing Congressus Numerantium, vol. 42, pp. 149160, 1984.
[6] T.M.G. Fruchterman and E. Reingold, Graph Drawing by ForceDirected Placement SoftwarePractice and Experience, vol. 21, pp. 11291164, 1991.
[7] E. Gansner, E. Koutsofios, and S. North, Drawing Graphs withdot, AT&T LabsResearch,http://www.research.att.com/sw/toolsgraphviz , 2002.
[8] G.H. Golub and C.F. Van Loan, Matrix Computations. Baltimore: Johns Hopkins Univ. Press, 1996.
[9] K.M. Hall, AnrDimensional Quadratic Placement Algorithm Management Science, vol. 17, pp. 219229, 1970.
[10] M. Jünger and P. Mutzel, Exact and Heuristic Algorithms for 2Layer Straightline Crossing Minimization Proc. Graph Drawing (GD '95), pp. 337348, 1995.
[11] T. Kamada and S. Kawai, An Algorithm for Drawing General Undirected Graphs Information Processing Letters, vol. 31, pp. 715, 1989.
[12] T. Kamps, J. Kleinz, and J. Read, ConstraintBased SpringModel Algorithm for Graph Layout Proc. Graph Drawing (GD '95), pp. 349360, 1995.
[13] Drawing Graphs: Methods and Models, M. Kaufmann and D. Wagner, eds. Springer Verlag, 2001.
[14] Y. Koren, On Spectral Graph Drawing Proc. Int'l Computing and Combinatorics Conf. (COCOON '03), pp. 496508, 2003.
[15] Y. Koren and D. Harel, AxisbyAxis Stress Minimization Proc. Graph Drawing (GD '03), 2003.
[16] Y. Koren, L. Carmel, and D. Harel, ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs Proc. IEEE Symp. Information Visualization 2002 (InfoVis 2002), pp. 137144, 2002.
[17] Y. Koren, L. Carmel, and D. Harel, Drawing Huge Graphs by Algebraic Multigrid Optimization Multiscale Modeling and Simulation, SIAM, to appear.
[18] Y. Koren and D. Harel, A MultiScale Algorithm for the Linear Arrangement Problem Proc. Graph Theoretical Concepts in Computer Science 2002 (WG '02), pp. 293306, 2002.
[19] R. Milo, S. ShenOrr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Network Motifs: Simple Building Blocks of Complex Networks Science, vol. 298, pp. 824827, 2002.
[20] K. Sugiyama and K. Misue, A Simple and Unified Method for Drawing Graphs: MagneticSpring Algorithm Proc. Graph Drawing (GD '94), pp. 364375, 1995.
[21] K. Sugiyama, S. Tagawa, and M. Toda, Methods for Visual Understanding of Hierarchical Systems IEEE Trans. Systems, Man, and Cybernetics, vol. 11, pp. 109125, 1981.
[22] W.T. Tutte, How to Draw a Graph Proc. London Math. Soc., vol. 13, pp. 743768, 1963.
[23] The Matrix Market collection,math.nist.govMatrixMarket, 2003.