A Multi-dimensional Approach to Force-Directed Layouts of Large Graphs

We present a novel hierarchical force-directed method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higher-dimensional embedding into a two or three dimensional subspace of E. Projecting high-dimensional drawings onto two or three dimensions often results in drawings that are "smoother" and more symmetric. Among the other notable features of our approach are the utilization of a maximal independent set filtration of the set of vertices of a graph, a fast energy function minimization strategy, efficient memory management, and an intelligent initial placement of vertices. Our implementation of the algorithm can draw graphs with tens of thousands of vertices using a negligible amount of memory in less than one minute on a mid-range PC.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  N. Quinn,et al.  A forced directed component placement procedure for printed circuit boards , 1979 .

[3]  J. G. Hollands,et al.  Engineering Psychology and Human Performance , 1984 .

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

[5]  Teofilo F. GONZALEZ,et al.  Clustering to Minimize the Maximum Intercluster Distance , 1985, Theor. Comput. Sci..

[6]  G. W. Furnas,et al.  Generalized fisheye views , 1986, CHI '86.

[7]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[8]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[9]  Kozo Sugiyama,et al.  Visualization of structural information: automatic drawing of compound digraphs , 1991, IEEE Trans. Syst. Man Cybern..

[10]  A. Brandt.  Multilevel computations of integral transforms and particle interactions with oscillatory kernels , 1991 .

[11]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[12]  A. Brandt.  Multigrid methods in lattice field computations , 1992, hep-lat/9204014.

[13]  Colin Ware,et al.  Visualizing object oriented software in three dimensions , 1993, CASCON.

[14]  Manojit Sarkar,et al.  Graphical fisheye views , 1994, CACM.

[15]  Andreas Ludwig,et al.  A Fast Adaptive Layout Algorithm for Undirected Graphs , 1994, GD.

[16]  Alvis Brazma,et al.  A Simple Algorithm for Drawing Large Graphs on Small Screens , 1994, Graph Drawing.

[17]  Ioannis G. Tollis,et al.  Algorithms for Drawing Graphs: an Annotated Bibliography , 1988, Comput. Geom..

[18]  Burkhard Monien,et al.  A Parallel Simulated Annealing Algorithm for Generating 3D Layouts of Undirected Graphs , 1995, GD.

[19]  Arne Frick,et al.  Fast Interactive 3-D Graph Visualization , 1995, GD.

[20]  Isabel F. Cruz,et al.  3D Graph Drawing with Simulated Annealing , 1995, GD.

[21]  Robert F. Cohen,et al.  How to Draw a Planar Clustered Graph , 1995, COCOON.

[22]  David Harel,et al.  Drawing graphs nicely using simulated annealing , 1996, TOGS.

[23]  Peter Eades,et al.  Multilevel Visualization of Clustered Graphs , 1996, GD.

[24]  Xuemin Lin,et al.  Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs , 1996, Graph Drawing.

[25]  Antonios Symvonis,et al.  Two Algorithms for Three Dimensional Orthogonal Graph Drawing , 1996, GD.

[26]  Ioannis G. Tollis,et al.  Incremental Orthogonal Graph Drawing in Three Dimensions , 1997, GD.

[27]  Jonathan D. Cohen,et al.  Drawing graphs to convey proximity: an incremental arrangement method , 1997, TCHI.

[28]  Therese C. Biedl,et al.  Three Approaches to 3D-Orthogonal Box-Drawings , 1998, GD.

[29]  Michael T. Goodrich,et al.  Balanced Aspect Ratio Trees and Their Use for Drawing Very Large Graphs , 1998, GD.

[30]  Emden R. Gansner,et al.  Improved Force-Directed Layouts , 1998, GD.

[31]  David R. Wood,et al.  Multi-dimensional Orthogonal Graph Drawing with Small Boxes , 1999, GD.

[32]  Michael T. Goodrich,et al.  Balanced Aspect Ratio Trees and Their Use for Drawing Large Graphs , 2000, J. Graph Algorithms Appl..

[33]  David Harel,et al.  A fast multi-scale method for drawing large graphs , 2000, AVI '00.

[34]  Chris Walshaw,et al.  Journal of Graph Algorithms and Applications a Multilevel Algorithm for Force-directed Graph-drawing , 2022 .

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

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

[37]  David Harel,et al.  A multi-scale algorithm for drawing graphs nicely , 2001, Discret. Appl. Math..