Spectral analysis of Internet topologies

Spectral analysis of the Internet topology at the autonomous system (AS) level, by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology is performed. We observe that the method suggests clusters of ASs with natural semantic proximity, such as geography or business interests. We examine how these clustering properties vary in the core and in the edge of the network, as well as across geographic areas, over time, and between real and synthetic data. We observe that these clustering properties may be suggestive of traffic patterns and thus have direct impact on the link stress of the network. Finally, we use the weights of the eigenvector corresponding to the first eigenvalue to obtain an alternative hierarchical ranking of the ASs.

[1]  Kenneth L. Calvert,et al.  Modeling Internet topology , 1997, IEEE Commun. Mag..

[2]  Santosh S. Vempala,et al.  Latent semantic indexing: a probabilistic analysis , 1998, PODS '98.

[3]  Sugih Jamin,et al.  Inet: Internet Topology Generator , 2000 .

[4]  Anna R. Karlin,et al.  Spectral analysis of data , 2001, STOC '01.

[5]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[6]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[7]  Jon M Kleinberg,et al.  Hubs, authorities, and communities , 1999, CSUR.

[8]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[9]  T. Erlebach,et al.  A Spectral Analysis of the Internet Topology , 2001 .

[10]  K. Goh,et al.  Spectra and eigenvectors of scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Lixin Gao,et al.  On inferring autonomous system relationships in the Internet , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[12]  Randy H. Katz,et al.  Characterizing the Internet hierarchy from multiple vantage points , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[13]  Santosh S. Vempala,et al.  Latent Semantic Indexing , 2000, PODS 2000.

[14]  Christos H. Papadimitriou,et al.  On the Eigenvalue Power Law , 2002, RANDOM.

[15]  Prabhakar Raghavan,et al.  Information retrieval algorithms: a survey , 1997, SODA '97.

[16]  Chris Ding,et al.  On the Use of Singular Value Decomposition for Text Retrieval , 2000 .

[17]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[18]  Ibrahim Matta,et al.  On the geographic location of internet resources , 2002, IMW '02.

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

[20]  Gene H. Golub,et al.  Matrix computations , 1983 .

[21]  Walter Willinger,et al.  The origin of power laws in Internet topologies revisited , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[22]  Alistair Sinclair,et al.  Algorithms for Random Generation and Counting: A Markov Chain Approach , 1993, Progress in Theoretical Computer Science.

[23]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[24]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[25]  Ibrahim Matta,et al.  On the origin of power laws in Internet topologies , 2000, CCRV.

[26]  Ellen W. Zegura,et al.  How to model an internetwork , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[27]  Fan Chung Graham,et al.  A random graph model for massive graphs , 2000, STOC '00.

[28]  J M Carlson,et al.  Highly optimized tolerance: a mechanism for power laws in designed systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Ellen W. Zegura,et al.  A quantitative comparison of graph-based models for Internet topology , 1997, TNET.

[30]  Christos H. Papadimitriou,et al.  Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet , 2002, ICALP.

[31]  L. Lovász.  Combinatorial problems and exercises , 1979 .

[32]  A. Barabasi,et al.  Spectra of "real-world" graphs: beyond the semicircle law. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Donald F. Towsley,et al.  On distinguishing between Internet power law topology generators , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[34]  BERNARD M. WAXMAN,et al.  Routing of multipoint connections , 1988, IEEE J. Sel. Areas Commun..

[35]  Walter Willinger,et al.  Network topology generators: degree-based vs. structural , 2002, SIGCOMM '02.

[36]  Ibrahim Matta,et al.  On the geographic location of Internet resources , 2003, IEEE J. Sel. Areas Commun..

[37]  Hawoong Jeong,et al.  Modeling the Internet's large-scale topology , 2001, Proceedings of the National Academy of Sciences of the United States of America.