Large scale networks fingerprinting and visualization using the k-core decomposition

We use the k-core decomposition to develop algorithms for the analysis of large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structural properties of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm, O(n + e), where n is the size of the network, and e is the number of edges, makes it suitable for the visualization of very large sparse networks. We show how the proposed visualization tool allows to find specific structural fingerprints of networks.

[1]  Vladimir Batagelj,et al.  Generalized Cores , 2002, ArXiv.

[2]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[3]  Stefan Wuchty,et al.  Peeling the yeast protein network , 2005, Proteomics.

[4]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[5]  Ramesh Govindan,et al.  Heuristics for Internet map discovery , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[6]  Alessandro Vespignani,et al.  k-core decomposition: a tool for the analysis of large scale Internet graphs , 2005, ArXiv.

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

[8]  Gary D. Bader,et al.  An automated method for finding molecular complexes in large protein interaction networks , 2003, BMC Bioinformatics.

[9]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[10]  Ulrik Brandes,et al.  Journal of Graph Algorithms and Applications Visual Ranking of Link Structures , 2022 .

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[12]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

[13]  Ben Shneiderman,et al.  Why Not Make Interfaces Better than 3D Reality? , 2003, IEEE Computer Graphics and Applications.

[14]  S. Kanaya,et al.  Prediction of Protein Functions Based on K-Cores of Protein-Protein Interaction Networks and Amino Acid Sequences , 2003 .

[15]  Maurizio Patrignani,et al.  Dynamic Analysis of the Autonomous System Graph , 2004 .