Topology, Hierarchy, and Correlations in Internet Graphs

  • Romualdo Pastor-Satorras
  • Alexei Vázquez
  • Alessandro Vespignani
Part III Information Networks & Social Networks
Part of the Lecture Notes in Physics book series (LNP, volume 650)


We present a statistical analysis of different metrics characterizing the topological properties of Internet maps, collected at two different resolution scales: the router and the autonomous system level. The metrics we consider allow us to confirm the presence of scale-free signatures in several statistical distributions, as well as to show in a quantitative way the hierarchical nature of the Internet. Our findings are relevant for the development of more accurate Internet topology generators, which should include, along with the properties of the degree distribution, the hierarchical signatures reviewed in the present work.


Random Graph Autonomous System Degree Distribution Internet Topology Internet Router 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1. B. Bollobás, Modern Graph Theory, (Springer-Verlag, New York, 1998).Google Scholar
  2. 2. R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach, (Cambridge University Press, Cambridge, 2004).Google Scholar
  3. 3. M. Faloutsos, P. Faloutsos, and C. Faloutsos, ACM SIGCOMM ‘99, Comput. Commun. Rev. 29, 251 (1999).Google Scholar
  4. 4. R. Govindan and H. Tangmunarunkit, Proc. of IEEE Infocom 2000, Tel Aviv, IsraelGoogle Scholar
  5. 5. G. Caldarelli, R. Marchetti, and L. Pietronero, Europhys. Lett. 52, 386 (2000).Google Scholar
  6. 6. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001); A. Vázquez, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. E 65, 066130 (2002).Google Scholar
  7. 7. W. Willinger, R. Govindan, S. Jamin, V. Paxson, and S. Shenker, Proc. Natl. Acad. Sci USA 99 2573, (2002)Google Scholar
  8. 8. H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, and W. Willinger, Comput. Commun. Rev. 32, 76 (2002)Google Scholar
  9. 9. Q. Chen, H. Chang, R. Govindan, S. Jamin, S. J. Shenker, and W. Willinger, Proceedings of IEEE Infocom 2002, New York, USA.Google Scholar
  10. 10. A. Broido and K. C. Claffy, San Diego Proceedings of SPIE International symposium on Convergence of IT and Communication. Denver, CO. 2001Google Scholar
  11. 11. D. Vukadinovic, P. Huang and T. Erlebach in Innovative Internet Computing Systems (I2CS 2002) Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2002.Google Scholar
  12. 12. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).Google Scholar
  13. 13. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of networks: From biological nets to the Internet and WWW, (Oxford University Press, Oxford, 2003).Google Scholar
  14. 14. P. Erdös and P. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).Google Scholar
  15. 15. B. Bollobás, Random graphs (Academic Press, London, 1095).Google Scholar
  16. 16. A. Medina, I. Matta, and J. Byers, Comput. Commun. Rev. 30, 2 (2000).Google Scholar
  17. 17. A. Medina and I. Matta, BRITE: a flexible generator of Internet topologies”, Tech. Rep. BU-CS-TR-2000-005, Boston University, 2000.Google Scholar
  18. 18. C. Jin, Q. Chen, and S. Jamin, “INET: Internet topology generators”, Tech. Rep. CSE-TR-433-00, EECS Dept., University of Michigan, 2000.Google Scholar
  19. 19. The National Laboratory for Applied Network Research (NLANR), sponsored by the National Science Foundation, provides Internet routing related information based on BGP data (see Scholar
  20. 20. The Cooperative Association for Internet Data Analysis (CAIDA), located at the San Diego Supercomputer Center, provides measurements of Internet traffic metrics (see Scholar
  21. 21. Topology project, Electric Engineering and Computer Science Department, University of Michigan ( Scholar
  22. 22. Mapping the Internet within the SCAN project at the Information Sciences Institute ( Scholar
  23. 23. B. Cheswick and H. Burch, Internet mapping project at Lucent Bell Labs ( Scholar
  24. 24. H. Burch and B. Cheswick, IEEE computer, 32, 97 (1999).Google Scholar
  25. 25. D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998).Google Scholar
  26. 26. H. Chou, ( Scholar
  27. 27. R. A. Albert, H. Jeong, and A.-L. Barabási, Nature 406, 378 (2000); D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. 85, 5468 (2000); R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001).Google Scholar
  28. 28. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).Google Scholar
  29. 29. S. N. Dorogovtsev and J. F. F. Mendes, Advances in Physics 51, 1079 (2002).Google Scholar
  30. 30. L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, Proc. Natl. Acad. Sci. USA 97, 11149 (2000).Google Scholar
  31. 31. S. Mossa, M. Barthélémy, H. E. Stanley, and L. A. N. Amaral, Phys. Rev. Lett. 88, 138701 (2002).Google Scholar
  32. 32. M. E. J. Newman, Phys. Rev. E 64, 016131-1 (2001); 64, 016132-1 (2001)Google Scholar
  33. 33. U. Brandes, Journal of Math. Sociology, 25, 35 (2001).Google Scholar
  34. 34. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. 87, 278201 (2001).Google Scholar
  35. 35. E. Ravasz and A. Barabási, Phys. Rev. E 67, 026112 (2003).Google Scholar
  36. 36. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. 88, 108701 (2002).Google Scholar
  37. 37. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).Google Scholar

Authors and Affiliations

  • Romualdo Pastor-Satorras
    • 1
  • Alexei Vázquez
    • 2
  • Alessandro Vespignani
    • 3
  1. 1.Department de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord, 08034 BarcelonaSpain
  2. 2.Department of Physics, University of Notre Dame, Notre Dame, IN 46556USA
  3. 3.Laboratoire de Physique Théorique, Bâtiment 210 Université de Paris-Sud 91405 ORSAY CedexFrance

Personalised recommendations