The Study on the Hierarchy of Internet Router-Level Topology

Jun ZHANG, Hai ZHAO, Chao LI, Xin GE

College of Information Science and Engineering, Northeastern University, Shenyang, China.

DOI: 10.4236/ijcns.2009.24032                

Abstract

Being a huge system, Internet topology structure is very complex. It can’t be treated as a plane simply, and its hierarchy must be analyzed. We used the k-core decomposition to disentangle the hierarchical structure of Internet Router-level topology. By analyzing the router-lever Internet topology measuring data from CAIDA (The Cooperative Association for Internet Data Analysis) ,we studied the characteristics of the nodes in the inner hierarchy and outer hierarchy respectively. The frequency-degree power law of the nodes which core-ness is lower and the regionally distribution of the nodes which coreness is higher were concluded. At last, the topology of every hierarchy was described by giving their figures. These descriptions can provide a valuable reference for modeling on the Internet topology.

Keywords

Complex Network, Hierarchy, Coreness, Power Law, Regionally, Internet

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	X. F. Wang, X. Li, and G. R. Chen, “The theory and application of complex network,” TsingHua University Press, Beijing, 2006.
[2]	D. Magoni and J. J. Pansiot, “Internet topology modeler based on map sampling,” Proceedings of the ISCC 2002, Taormina, IEEE, pp. 1021-1027, 2002.
[3]	J. Winick and S. Jamin., “Inet-3.0: Internet topology gen-erator,” Technical Report, CSE-TR-456-02, Ann Arbor: University of Michigan, 2002.
[4]	D. Magoni, “A software for network topology analysis and modeling,” Proceedings of the MASCOTS 2002. IEEE Computer Society, pp. 364-371, 2002.
[5]	S. Zhouu and R. J. Mondragon, “Accurately modeling the Internet topology,” Physical Review Letters, Vol. 70, pp. 106-108, 2004.
[6]	S. Zhouu and R J. Mondragon, “Towards modeling the Internet topology-the interactive growth model,” Teletraffic science and engineering, Vol. 5, pp. 121-130, 2003.
[7]	S. Zhouu and R J. Mondragon, “The rich-club phenomenon in the Internet topology,” IEEE Communication Let-ters, Vol.8, No.3, pp. 180-182, 2004.
[8]	S. T. Park, D. M. Pennock, and C. L. Giles, “Comparing static and dynamic measurements and models of the Internet’s topology,” Proceedings of the 23rd Annual Joint Conference of the IEEE Computer and Communi-cations Societies, pp. 1616-1627, March 2004.
[9]	G. Chen, Z. P. Fan, and X. Li, “Modeling the complex Internet topology,” Complex Dynamics in Communication Networks, G. Vattay, L. Kocarev (Eds), Berlin, Springer-Verlag, 2005.
[10]	D. Vukadinovic, P. Huang, and T. Erlebach, “On the spectrum and structure of Internet topology graphs,” Proceedings of the Innovative Internet Computing Systems (I2CS), LNCS 2346, Berlin, Springer-Verlag, pp. 83-95, 2002.
[11]	Y. Zhang, H. L. Zhang, and B. X. Fang, “A survey on internet topology modeling”, Journal of Software, Vol. 15, pp. 1220-1226, 2004.
[12]	Macroscopic Topology Measurements, CAIDA. http:// www.caida.org/analysis/topology/macroscopic/.
[13]	K. Calvert, M. Doar, and E. Zegura, “Modeling Internet topology”, IEEE Communication Magazine, Vol. 35, pp. 160-163, 1997.
[14]	J. I. Alvarez-Hamelin, et al., “k-core decomposition: A tool for the visualization of large scale networks,” Arxiv preprint cs. NI/0504107, 2005.
[15]	J. Zhang, H. Zhao, and Y. Zhou, “Relationship between degree and core number of Internet nodes at router level,” Journal of Northeastern University (Natural Science), Vol. 29, No.5, pp. 653-656, 2008.
[16]	B. Cheswick, H. Burch, and S. Branigan, “Mapping and visualizing the Internet,” in Proceedings of the 2000 USENIX Ann Technical Conference, San Diego, California, USA, June 2000.