Weighted spectral distribution for internet topology analysis: Theory and applications

IEEE/ACM Transactions on Networking

Volumn 18, Issue 1, 2010, Pages 164-176

  Fay, Damien ^a,b   Haddadi, Hamed ^a,c   Thomason, Andrew ^a   Moore, Andrew W ^a   Mortier, Richard ^d   Jamakovic, Almerima ^e   Uhlig, Steve ^f   Rio, Miguel ^g  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b MCGILL UNIVERSITY   (Canada)

^c MAX PLANCK INSTITUTE FOR SOFTWARE SYSTEMS   (Germany)

^d Vipadia Limited   (United Kingdom)

^e TNO   (Netherlands)

^f TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^g UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Graph metrics; Internet topology; Spectral graph theory; Topology generation

Indexed keywords

INTERNET CORE; INTERNET TOPOLOGIES; LARGE-SCALE MEASUREMENT; MIXING PROPERTY; PARAMETERIZATIONS; SPECTRAL DISTRIBUTION; SPECTRAL GRAPH THEORY; STRUCTURAL COMPARISON; STRUCTURAL SIMILARITY; SYNTHETIC NETWORKS; SYNTHETIC TOPOLOGY; TOPOLOGY GENERATION;

GRAPH THEORY;

INTERNET;

EID: 77249117640     PISSN: 10636692     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNET.2009.2022369     Document Type: Article

References (41)

1. H. Bunke, "Graph matching: Theoretical foundations, algorithms, and applications," in Proc. Int. Conf. Vision Interface, May 2000, pp. 82-88.
2. V. Kann, "On the approximability of the maximum common subgraph problem," in Proc. 9th Annu. Symp. Theor. Aspects Comput. Sci., 1992, pp. 377-388.
3. S. Hanna, "Representation and generation of plans using graph spectra," presented at the 6th Int. Space Syntax Symp., Istanbul, Turkey, 2007.
4. B. Luo and E. Hancock, "Structural graph matching using the em algorithm and singular value decomposition," IEEE Trans. Pattern Anal. Machine Intell., vol.23, no.10, pp. 1120-1136, Oct. 2001.
5. A. Ng, M. Jordan, and Y. Weiss, "On spectral clustering: analysis and an algorithm," in Advances in Neural Information Processing Systems 14, T. Dietterich, S. Becker, and Z. Ghahramani, Eds. Cambridge, MA: MIT Press, 2002.
6. H. Haddadi, D. Fay, S. Uhlig, A. Moore, R. Mortier, A. Jamakovic, and M. Rio, "Tuning topology generators using spectral distributions," in SPEC Int. Perform. Eval. Workshop, Darmstadt, Germany, 2008, vol.5119, Lecture Notes in Computer Science, pp. 154-173.
7. C. Gkantsidis, M. Mihail, and E. Zegura, "Spectral analysis of Internet topologies," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 2003, pp. 364-374.
8. S.Butler, Lecture Notes for Spectral Graph Theory. Tianjin, China,: Nankai Univ., 2006.
9. A. Jamakovic and S. Uhlig, "On the relationship between the algebraic connectivity and graph's robustness to node and link failures," in Proc. 3rd Conf. Next Gen. Internet Networks (EuroNGI), Trondheim, Norway, 2007, pp. 96-102.
10. D. Vukadinovic, P. Huang, and T. Erlebach, "On the spectrum and structure of Internet topology graphs," in Proc. 2nd Int. Workshop IICS, 2002, pp. 83-95.
11. J. Winick and S. Jamin, "Inet-3.0: Internet topology generator," Univ. of Michigan, Tech. Rep. CSE-TR-456-502, 2002.
12. S. V. N. Vishwanathan, K. Borgwardt, and N. Schraudolph, "Fast computation of graph kernels," in Advances in Neural Information Processing Systems 19 (NIPS 2006). Cambridge, MA: MIT Press, 2006.
13. L. Shyu, S.-Y. Lau, and P. Huang, "On the search of Internet as-level topology invariants," in Proc. IEEE GLOBECOM, San Francisco, CA, 2006, pp. 1-5.
14. M. Latapy and C. Magnien, "Complex network measurements: Estimating the relevance of observed properties," in Proc. IEEE INFOCOM, Apr. 2008, pp. 1660-1668.
15. X. Wang and D. Loguinov, "Wealth-based evolution model for the Internet as-level topology," in Proc. IEEE INFOCOM, Apr. 2006, pp. 1-11.
16. A. Wool and G. Sagie, "A clustering approach for exploring the Internet structure," in Proc. 23rd IEEE Conv. Electr. Electron. Eng. Israel, Sep. 2004, pp. 149-152.
17. Y. Li, J.-H. Cui, D. Maggiorini, and M. Faloutsos, "Characterizing and modelling clustering features in as-level Internet topology," in Proc. IEEE INFOCOM, Apr. 2008, pp. 271-275.
18. A. Seary and W. Richards, "Spectral methods for analyzing and visualizing networks: An introduction," in Dynamic Social Network Modeling and Analysis. Washington, DC: National Academies Press, 2003, pp. 209-228.
19. B. Nadler, S. Lafon, R. Coifman, and I. Kevrekidis, "Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators," in Proc. NIPS, 2005, pp. 955-962.
20. A. G. Thomason, "Pseudo-random graphs," in Random Graphs '85, ser. North-Holland Mathematical Studies. Amsterdam, The Netherlands: Elsevier, 1987, vol.144, pp. 307-331.
21. F. R. K. Chung, R. L. Graham, and R. M. Wilson, "Pseudo-random graphs," Combinatorica, vol.9, no.4, pp. 345-362, 1989.
22. F. R. K. Chung, Spectral Graph Theory, ser. CBMS Regional Conference Series in Mathematics. Providence, RI: AMS, 1997.
23. R. Albert and A.-L. Barabasi, "Topology of evolving networks: local events and universality," Phys. Rev. Lett., vol.85, p. 5234, 2000.
24. S. Butler, "Interlacing for weighted graphs using the normalized lapla-cian," Electron. J. Linear Algebra, vol.16, pp. 90-98, 2007.
25. B. Huffaker, D. Andersen, E. Aben, M. Luckie, K. Claffy, and C. Shannon, "The Skitter AS links dataset," 2001-2007 [Online. Available: http://www.caida.org/data/active/skitter-aslinks-dataset.xml/
26. R. Oliveira, B. Zhang, and L. Zhang, "Observing the evolution of Internet as topology," in Proc. ACM SIGCOMM, Kyoto, Japan, Aug. 2007, pp. 313-324.
27. R. Bush, J. Hiebert, O. Maennel, M. Roughan, and S. Uhlig, "Testing the reachability of (new) address space," in Proc. SIGCOMM Workshop INM, 2007, pp. 236-241.
28. A. Lakhina, J. Byers, M. Crovella, and P. Xie, "Sampling biases in IP topology measurements," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 2003, pp. 332-341.
29. M. Newman, "Assortative mixing in networks," Phys. Rev. Lett., vol.89, no.20, pp. 871-898, 2002.
30. H. Haddadi, D. Fay, A. Jamakovic, O. Maennel, A. W. Moore, R. Mortier, M. Rio, and S. Uhlig, "Beyond node degree: Evaluating AS topology models," Computer Lab., Univ. of Cambridge, U.K., Tech. Rep. UCAM-CL-TR-725, 2008.
31. P. Gill, M. Arlitt, Z. Li, and A. Mahanti, "The flattening Internet topology: Natural evolution, unsightly barnacles or contrived collapse?," in Proc. PAM, Apr. 2008, pp. 1-10.
32. J. I. Alvarez-Hamelin, L. Dall'Asta, A. Barrat, and A. Vespignani, "A'-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases," Netw. Hetero. Media, vol.3, pp. 371-371, 2008.
33. E. W. Zegura, K. L. Calvert, and M. J. Donahoo, "A quantitative comparison of graph-based models for Internet topology," IEEE/ACM Trans. Netw., vol.5, no.6, pp. 770-783, Dec. 1997.
34. T. Bu and D. Towsley, "On distinguishing between Internet power law topology generators," in Proc. IEEE INFOCOM, New York, Jun. 2002, pp. 638-647.
35. B. M. Waxman, "Routing of multipoint connections," IEEE J. Sel. Areas Commun., vol.6, pp. 1617-1622, Dec. 1988.
36. S. Zhou, "Characterising and modelling the Internet topology, the rich-club phenomenon and the PFP model," BT Technol. J., vol.24, pp. 108-115, 2006.
37. P. Mahadevan, D. Krioukov, M. Fomenkov, X. Dimitropoulos, K. C. Claffy, and A. Vahdat, "The Internet as-level topology: Three data sources and one definitive metric," Comput. Commun. Rev., vol.36, no.1, pp. 17-26, 2006.
38. J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J., vol.7, pp. 308-313, 1965.
39. J. Dennis and D. Woods, "Optimization in microcomputers: The nelder-meade simplex algorithm," in New Computing Environments: Microcomputers in Large-Scale Computing, A. Wouk, Ed. Philadelphia, PA: SIAM, 1987, pp. 116-122.
40. P. Zhu and C. Wilson, "A studyof graph spectra for comparing graphs," presented at the 16th BMVC, Sep. 2005.
41. A.N.Kolmogorov and S. V. Fomin, Introductory Real Analysis. New York: Dover, 1975.