A Power-Law Approach on Router-Level Internet Macroscopic Topology Modeling

  • Ye Xu
  • Wen-bo Zhang
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 62)


With the giant samples of router-level Internet macroscopic topology, obvious power-law properties were found after approaches such as frequency-degree power-law, degree-rank power-law and CCDF(d)-degree power-law distributions were studied and applied. The frequency-degree power-law relationship is found to be with a power exponent of 2.1406. The degree-rank power-law, however, is found to have two phases with power-exponents of 0.29981 and 0.84639 respectively. And the CCDF(d)-degree power-law property was proved not to exist in the measured Internet topology after compared with the Weibull distribution. With these, especially the two-phase degree-rank power-law power-exponents, we began to construct an Internet topology model (IBA model) by improving and optimizing the traditional BA model to fit the measured samples. Algorithm for the IBA model was finally given.


Power-law analysis Internet topology modeling BA model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. ACM SIGCOMM ComputerCommunication Review 29(4), 251–262 (1999)CrossRefGoogle Scholar
  2. 2.
    Jiang, Y., Fang, B.X., Hu, M.Z.: An Example of Analyzing the Characteristics of a Large Scale ISP Topology Measured from Multiple Vantage Points. Journal of Software 16(5), 846–856 (2005)CrossRefGoogle Scholar
  3. 3.
    Siganos, G., Faloutsos, M., Faloutsos, P., Faloutsos, C.: Power laws and the AS-level Internet topology. IEEE/ACM Trans. on Networking 11(4), 514–524 (2003)CrossRefGoogle Scholar
  4. 4.
    Siganos, G., Faloutsos, M., Faloutsos, C.: The Evolution of the Internet: Topology and Routing,
  5. 5.
    Sagy, B., Mira, G., Avishai, W.: An incremental super-linear preferential internet topology model. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 53–62. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Lakhina, A., Byers, J.W., Crovella, M., Xie, P.: Sampling biases in IP topology measurements. In: Proc. of the IEEE INFOCOM 2003, San Francisco, vol. 1, pp. 332–341 (2003)Google Scholar
  7. 7.
    Wang, X.F., Li, X., Chen, G.R.: Complex networks theory and its application, pp. 49–70. QsingHua Press, Beijing (2006)Google Scholar
  8. 8.
    Sagy, B., Mira, G., Avishai, W.: A geographic directed preferential Internet topology mode. Arxiv:CS, NI/0502061 (2005)Google Scholar
  9. 9.
    Cao, L.B., Dai, R.W.: The intelligent Information System—Internet, pp. 121–130. Science Press, Beijing (2001)Google Scholar
  10. 10.
    Broido, A., Claffy, K.C.: Internet topology: Connectivity of IP graphs. In: Fahmy, S., Park, K. (eds.) Scalability and Traffic Control in IP Networks. Proc. of the SPIE ITCom, vol. #4526, pp. 172–187. SPIE Press, Washington (2001)Google Scholar
  11. 11.
    Spring, N., Mahajan, R., Wetherall, D.: Measuring ISP topologies with rocketfuel. ACM SIGCOMM Computer Communication Review 32(4), 133–145 (2002)CrossRefGoogle Scholar
  12. 12.
    Waxman, B.M.: Routing of multipoint connections. IEEE Journal on Selected Areas in Communications 6(9), 1617–1622 (1988)CrossRefGoogle Scholar
  13. 13.
    Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of Growing Random Networks. Phys. Rev. Lett. 85, 4629–4632 (2000)CrossRefGoogle Scholar
  14. 14.
    Zhang, W.B.: Research on the Life Characteristic and Evolution of Internet macroscopic Topology, pp. 6–23, 49–67. Northeastern University, Shenyang (2005)Google Scholar
  15. 15.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Chen, Q., Chang, H., Govindan, R., Jamin, S.: The origin of power laws in Internet topologies revisited. In: Proc. of the IEEE INFOCOM, New York, vol. 2, pp. 608–617 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ye Xu
    • 1
  • Wen-bo Zhang
    • 1
  1. 1.College of Information Science and EngineeringShenyang Ligong UniversityShenyangChina

Personalised recommendations