Distributed location of the critical nodes to network robustness based on spectral analysis

We propose a methodology to locate the most critical nodes to network robustness in a fully distributed way. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a limited neighborhood around each node in the network. We also present a procedure allowing the navigation from any node towards a critical node following only local information computed by the proposed algorithm. Experimental results confirm the effectiveness of our proposal considering networks of different scales and topological characteristics.

[1]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[2]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[3]  David Kotz,et al.  Localized Bridging Centrality for Distributed Network Analysis , 2008, 2008 Proceedings of 17th International Conference on Computer Communications and Networks.

[4]  Ljupco Kocarev,et al.  Network science: A new paradigm shift , 2010, IEEE Network.

[5]  Anne-Marie Kermarrec,et al.  Second order centrality: Distributed assessment of nodes criticity in complex networks , 2011, Comput. Commun..

[6]  Peter V. Marsden,et al.  Egocentric and sociocentric measures of network centrality , 2002, Soc. Networks.

[7]  Amin Saberi,et al.  On certain connectivity properties of the Internet topology , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[8]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[9]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[10]  Guanhua Yan,et al.  Criticality analysis of Internet infrastructure , 2010, Comput. Networks.

[11]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[12]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[13]  Yan Shi,et al.  Critical nodes detection in mobile ad hoc network , 2006, 20th International Conference on Advanced Information Networking and Applications - Volume 1 (AINA'06).

[14]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[15]  Ted G. Lewis,et al.  Network Science: Theory and Applications , 2009 .

[16]  Fan R. K. Chung,et al.  Lectures on Spectral Graph Theory , 2001 .

[17]  A. Jamakovic,et al.  On the relationship between the algebraic connectivity and graph's robustness to node and link failures , 2007, 2007 Next Generation Internet Networks.

[18]  Shi Xiao,et al.  Tolerance of intentional attacks in complex communication networks , 2008, IEEE Communications Magazine.

[19]  Taieb Znati,et al.  On Approximation of New Optimization Methods for Assessing Network Vulnerability , 2010, 2010 Proceedings IEEE INFOCOM.

[20]  A. Leon-Garcia,et al.  Comparison of network criticality, algebraic connectivity, and other graph metrics , 2009, SIMPLEX '09.

[21]  Miguel Rio,et al.  Weighted Spectral Distribution for Internet Topology Analysis: Theory and Applications , 2010, IEEE/ACM Transactions on Networking.

[22]  Christos Gkantsidis,et al.  Spectral analysis of Internet topologies , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[23]  Muriel Médard,et al.  Robustness in large-scale random networks , 2004, IEEE INFOCOM 2004.

[24]  Jin-Qing Fang,et al.  Network Science—Theory and Application , 2010 .

[25]  Ana Paula Couto da Silva,et al.  On the joint dynamics of network diameter and spectral gap under node removal , 2010 .

[26]  Jin-Qing Fang,et al.  Network Science - Theory and Application , 2010, J. Assoc. Inf. Sci. Technol..

[27]  Ivan Stojmenovic,et al.  Localized Algorithms for Detection of Critical Nodes and Links for Connectivity in Ad hoc Networks , 2004 .

[28]  D. Spielman Algorithms, Graph Theory, and Linear Equations in Laplacian Matrices , 2011 .

[29]  B. Mohar THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .