Near-Optimal Concentric Circles Layout

The majority of graph visualization algorithms emphasize improving the readability of graphs by focusing on various vertex and edge rendering techniques. However, revealing the global connectivity structure of a graph by identifying significant vertices is an important and useful part of any graph analytics system. Centrality measures reveal the “most important” vertices of a graph, commonly referred to as central or influential vertices. Hence, a centrality-oriented visualization may highlight these important vertices and give deep insights into graph data. This paper proposes a mathematical optimization-based clustered graph layout called Near-Optimal Concentric Circles (NOCC) layout to visualize medium to large scale-free graphs. We cluster the vertices by their betweenness values and optimally place them on concentric circles to reveal the extensive connectivity structure of the graph while achieving aesthetically pleasing layouts. Besides, we incorporate different edge rendering techniques to improve graph readability and interaction.

[1]  Ulrik Brandes,et al.  Drawing the AS Graph in 2.5 Dimensions , 2004, GD.

[2]  Mithileysh Sathiyanarayanan,et al.  Social network visualization: Does partial edges affect user comprehension? , 2017, 2017 9th International Conference on Communication Systems and Networks (COMSNETS).

[3]  M. Newman Power laws, Pareto distributions and Zipf's law , 2005 .

[4]  Karsten Klein,et al.  Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization , 2015, IEEE Computer Graphics and Applications.

[5]  Michal Zabovsky,et al.  Radius degree layout — Fast and easy graph visualization layout , 2014, The 10th International Conference on Digital Technologies 2014.

[6]  Giuseppe Liotta,et al.  Partial edge drawing: Homogeneity is more important than crossings and ink , 2016, 2016 7th International Conference on Information, Intelligence, Systems & Applications (IISA).

[7]  Christopher Leckie,et al.  Visualisation of power-law network topologies , 2003, The 11th IEEE International Conference on Networks, 2003. ICON2003..

[8]  Jia-Kai Chou,et al.  PaperVis: Literature Review Made Easy , 2011, Comput. Graph. Forum.

[9]  Enrico Bertini,et al.  Social Networks Visualization : A Brief Survey , 2005 .

[10]  Chunjie Zhou,et al.  Generating Scale-Free Topology for Wireless Neighborhood Area Networks in Smart Grid , 2019, IEEE Transactions on Smart Grid.

[11]  Navid Dianati,et al.  Unwinding the "hairball" graph: a pruning algorithm for weighted complex networks , 2015, Physical review. E.

[12]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[13]  Hans J. Herrmann,et al.  Revealing the structure of the world airline network , 2014, Scientific Reports.

[14]  Yoshi Fujiwara,et al.  Visualizing large-scale structure of a million-firms economic network , 2015, SIGGRAPH Asia Visualization in High Performance Computing.

[15]  Zhong Chen,et al.  The Scale-free Network of Passwords : Visualization and Estimation of Empirical Passwords , 2015, ArXiv.

[16]  D. Ingber,et al.  High-Betweenness Proteins in the Yeast Protein Interaction Network , 2005, Journal of biomedicine & biotechnology.

[17]  Bettina Speckmann,et al.  SolarView: Low Distortion Radial Embedding with a Focus , 2019, IEEE Transactions on Visualization and Computer Graphics.

[18]  Romain Bourqui,et al.  Fast Graph Drawing Algorithm Revealing Networks Cores , 2015, 2015 19th International Conference on Information Visualisation.

[19]  Mark Gerstein,et al.  The Importance of Bottlenecks in Protein Networks: Correlation with Gene Essentiality and Expression Dynamics , 2007, PLoS Comput. Biol..

[20]  Donald E. Knuth,et al.  Computer-drawn flowcharts , 1963, CACM.

[21]  Michael Garland,et al.  On the Visualization of Social and other Scale-Free Networks , 2008, IEEE Transactions on Visualization and Computer Graphics.

[22]  Michele Garetto,et al.  Social Network De-Anonymization Under Scale-Free User Relations , 2016, IEEE/ACM Transactions on Networking.

[23]  Fan Chung Graham,et al.  Drawing Power Law Graphs , 2004, GD.

[24]  Ulrik Brandes,et al.  Probabilistic Graph Layout for Uncertain Network Visualization , 2017, IEEE Transactions on Visualization and Computer Graphics.

[25]  Manuel J. Fonseca,et al.  Proceedings of the Joint Symposium on Computational Aesthetics and Sketch-Based Interfaces and Modeling and Non-Photorealistic Animation and Rendering , 2016 .

[26]  Colin Ware,et al.  Cognitive Measurements of Graph Aesthetics , 2002, Inf. Vis..

[27]  Seok-Hee Hong,et al.  Drawing Clustered Graphs in Three Dimensions , 2005, Graph Drawing.

[28]  Faramarz Samavati,et al.  Daisy visualization for graphs , 2016 .

[29]  M. Gerstein,et al.  Genomic analysis of essentiality within protein networks. , 2004, Trends in genetics : TIG.

[30]  P. Bork,et al.  Evolution of biomolecular networks — lessons from metabolic and protein interactions , 2009, Nature Reviews Molecular Cell Biology.

[31]  Haizhou Wang,et al.  Ckmeans.1d.dp: Optimal k-means Clustering in One Dimension by Dynamic Programming , 2011, R J..

[32]  Le Song,et al.  Visualisation and Analysis of Large and Complex Scale-free Networks , 2005, EuroVis.