FlexGD: A flexible force-directed model for graph drawing

We propose FlexGD, a force-directed algorithm for straightline undirected graph drawing. The algorithm strives to draw graph layouts encompassing from uniform vertex distribution to extreme structure abstraction. It is flexible for it is parameterized so that the emphasis can be put on either of the two drawing criteria. The parameter determines how much the edges are shorter than the average distance between vertices. Extending the clustering property of the LinLog model, FlexGD is efficient for cluster visualization in an adjustable level. The energy function of FlexGD is minimized through a multilevel approach, particularly designed to work in contexts where edge length distribution is not uniform. Applying FlexGD on several real datasets, we illustrate both the good quality of the layout on various topologies, and the ability of the algorithm to meet the addressed drawing criteria.

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

[2]  Yifan Hu,et al.  Efficient, High-Quality Force-Directed Graph Drawing , 2006 .

[3]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[4]  Charu C. Aggarwal,et al.  Graph Clustering , 2010, Encyclopedia of Machine Learning and Data Mining.

[5]  Y. Koren,et al.  Drawing graphs by eigenvectors: theory and practice , 2005 .

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

[7]  Afshin Moin,et al.  Recommendation And Visualization Techniques For large Scale Data. (Les Techniques De Recommandation Et De Visualisation Pour Les Données A Une Grande Echelle) , 2012 .

[8]  Jennifer A. Scott,et al.  A Multilevel Algorithm for Wavefront Reduction , 2001, SIAM J. Sci. Comput..

[9]  Martin G. Everett,et al.  Parallel Dynamic Graph Partitioning for Adaptive Unstructured Meshes , 1997, J. Parallel Distributed Comput..

[10]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

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

[12]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

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

[14]  Thomas Puppe.  Spectral Graph Drawing: A Survey , 2008 .

[15]  Daniel Tunkelang,et al.  JIGGLE: Java Interactive Graph Layout Environment , 1998, GD.

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

[17]  David Harel,et al.  A Fast Multi-scale Method for Drawing Large Graphs , 2000, Graph Drawing.

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

[19]  Vipin Kumar,et al.  Highly Scalable Parallel Algorithms for Sparse Matrix Factorization , 1997, IEEE Trans. Parallel Distributed Syst..

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

[21]  Michael Jünger,et al.  An Experimental Comparison of Fast Algorithms for Drawing General Large Graphs , 2005, GD.

[22]  Andreas Noack,et al.  Energy Models for Graph Clustering , 2007, J. Graph Algorithms Appl..

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