How to Draw a Graph, Revisited

W. T. Tutte published a paper in 1963 entitled “How to Draw a Graph”. Tutte’s motivation was mathematical, and his paper can be seen as a contribution to the long tradition of geometric representations of combinatorial objects. Over the following 40 odd years, the motivation for creating visual representations of graphs has changed from mathematical curiosity to Visual Analytics. Current demand for Graph Drawing methods is now high, because of the potential for more human-comprehensible visual forms in industries as diverse as Biotechnology, Homeland Security, and Sensor Networks. Many new methods have been proposed, tested, implemented, and found their way into commercial tools. This paper describes two strands of this history: the force directed approach, and the planarity approach. Both approaches originate in Tutte’s paper.

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

[2]  David Harel,et al.  ACE: a fast multiscale eigenvectors computation for drawing huge graphs , 2002, IEEE Symposium on Information Visualization, 2002. INFOVIS 2002..

[3]  Markus Chimani,et al.  The Open Graph Drawing Framework , 2013 .

[4]  J. A. Bondy,et al.  Progress in Graph Theory , 1984 .

[5]  Daniel Tunkelang,et al.  A Numerical Optimization Approach to General Graph Drawing , 1999 .

[6]  János Pach,et al.  How to draw a planar graph on a grid , 1990, Comb..

[7]  Hubert de Fraysseix,et al.  An Heuristic for Graph Symmetry Detection , 1999, GD.

[8]  Michael Jünger,et al.  The Open Graph Drawing Framework (OGDF) , 2013, Handbook of Graph Drawing and Visualization.

[9]  D. Rose,et al.  Generalized nested dissection , 1977 .

[10]  Hiroshi Nagamochi,et al.  Star-Shaped Drawings of Graphs with Fixed Embedding and Concave Corner Constraints , 2008, COCOON.

[11]  Helen C. Purchase,et al.  Which Aesthetic has the Greatest Effect on Human Understanding? , 1997, GD.

[12]  Tomihisa Kamada,et al.  Visualizing Abstract Objects and Relations , 1989, World Scientific Series in Computer Science.

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

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

[15]  Xuemin Lin,et al.  Spring algorithms and symmetry , 2000, Theor. Comput. Sci..

[16]  Walter Schnyder,et al.  Embedding planar graphs on the grid , 1990, SODA '90.

[17]  K. Wagner Bemerkungen zum Vierfarbenproblem. , 1936 .

[18]  Michael Jünger,et al.  Drawing Large Graphs with a Potential-Field-Based Multilevel Algorithm , 2004, GD.

[19]  L. Beineke,et al.  Selected Topics in Graph Theory 2 , 1985 .

[20]  Ulrik Brandes,et al.  Drawing on Physical Analogies , 2001, Drawing Graphs.

[21]  W. T. Tutte How to Draw a Graph , 1963 .

[22]  Hiroshi Nagamochi,et al.  An algorithm for constructing star-shaped drawings of plane graphs , 2010, Comput. Geom..

[23]  H. Whitney Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Richard C. Waters,et al.  A Short Note on the History of Graph Drawing , 2001, GD.

[25]  Goos Kant,et al.  Drawing planar graphs using the canonical ordering , 1996, Algorithmica.

[26]  Hiroshi Nagamochi,et al.  A Linear-Time Algorithm for Star-Shaped Drawings of Planar Graphs with the Minimum Number of Concave Corners , 2011, Algorithmica.

[27]  B. Bollobás Surveys in Combinatorics , 1979 .

[28]  Tutte's spring theorem , 2004 .

[29]  Leslie G. Valiant,et al.  Universality considerations in VLSI circuits , 1981, IEEE Transactions on Computers.

[30]  Vladimir P. Korzhik,et al.  Minimal Obstructions for 1‐Immersions and Hardness of 1‐Planarity Testing , 2009, J. Graph Theory.

[31]  Marek Chrobak,et al.  A Linear-Time Algorithm for Drawing a Planar Graph on a Grid , 1995, Inf. Process. Lett..

[32]  János Pach Geometric Graph Theory , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[33]  Yifan Hu,et al.  GMap: Visualizing graphs and clusters as maps , 2010, 2010 IEEE Pacific Visualization Symposium (PacificVis).

[34]  János Pach,et al.  Graphs drawn with few crossings per edge , 1997, Comb..

[35]  Huaming Zhang,et al.  Canonical Ordering Trees and Their Applications in Graph Drawing , 2005, Discret. Comput. Geom..

[36]  Grigorios A. Pavliotis,et al.  Multiscale Methods: Averaging and Homogenization , 2008 .

[37]  Stephen G. Kobourov,et al.  Force-Directed Drawing Algorithms , 2013, Handbook of Graph Drawing and Visualization.