Analysis Of Fractal Characteristic And Coarse-graining Of Internet Macroscopic Topology Structure

Being a typical instance of complex network, the research on Internet topology has become a hot topic at present and attracted more and more attention of academia. In recent years, researches in this field have made considerable progression, especially in the overall side. The coarse-grained renormalization and the fractal analysis on the Internet macroscopic topology can help people understand the relationship between the part and whole of the Internet much better, and it is significance for people to know the inner nature of the whole object by the limited and little information.The router-level and IP-level data in Feburary,2011which is used in this paper is collected from fifteen monitors of CAIDA (The Cooperative Association for Internet Data Analysis). We revised and merged the data so that we can make up the missing edges caused by the single point measurement and provide the correct data for the later chapers effectivily.Secondly, we renormalized the router-level data of IPv4in February2011and IP-level data of IPv6between December2008and February2011by the core-thresholding coarse-grained process. The qualitative analysis of degree distribution exponent and degree-related characteristics and the fractal dimension indicates that network with higher KC have no fractal feacture. Fractal is obvious or not is related to the links among the nodes with higher degree. And the differences of the features in the different KC networks depend on the assortative coefficient.Thirdly, this article renormalized the AS-level topology using the box-coverign method. We know that the AS-level network has fractal feacture also by analysing the fractal dimension and the pow-law exponention. By analysing degree feactures and connection of netwok, we conclude that the increase of average degree and maxdegree and links among the nodes with high degree caused the increase of the clustering cofficient. And the evolution trend of the coarse-grained network is similar to the original network. The central verteies have higher coreness and closeness centrary and robustness and lower degree in original network but have higher degree conversely in the renormalized netwrok. The peripheral verteiex in not only orginal network but also in renormalized network have lower degree and coreness and closeness centrary.Based on the fractal feacture of the Internet, people can know the overall trends by analysing a small amount of data. And it has a guiding significance on the re-design the Internet.