Research On The Fractal Characteristics Of Internet Macroscopic Topology

Internet is a typical instance of the complex network, and the characteristics analysis of its macro-topology and modeling is very important with extensive academic attention. In recent years, people in the research field have made considerable progress, especially in the autonomous system level (autonomous system, AS-level). Based on the large, authoritative, long time span, actual measuring data obtained from CAIDA, a partner of Northeastern University Embedded technology lab, of IPv6IP level, IPv4routing level and AS level topology,were selected from January2009to June2011in this article. Based on the data, the fractal characteristics research of the Internet topology is carried out in this paper by the coarse-grained the network. The main works in this paper are as follow:First of all, in this paper statistics of certain factors of the Internet in months was carried out, such as the number of nodes in the network, the number of connections, the average node degree, network maximum node degree and height, leaf and small values of node degree, average path length of the network capacity and other conventional features, In the selected time span under the evolution, the relationship between the features was studied. On the topic of the network connectivity, the rich man’s club and the clustering coefficient was analyzed. This paper also studied the power-law of the network, demonstrating that the power-law degree distribution line PDF and CCDF of power-law and exponential, respectively, as well as the PDF and CCDF of power of evolution, the results indices that the topology of "a few nodes have many connections" phenomenon gradually increase over time, which more clearly reflects the degree distribution level trend. In the analysis of the network level, we draw the conclusion that the trends are basically the same and the change of the number of the maximum coreness node lead to the fluctuations of the coreness by the evolution analysis of the network coreness and the node number of the maximum coreness. In the analysis of relation of the coreness and the degree number, the distribution of the degree meet the power-law while the degree number is not bigger than500. In the analysis of the degree distribution the same coreness node, the degree distribution of the lower corness node met the power-law.Second, this paper presents a new community-based topology model-CBTM. Against the characteristics of community structure of complex network, this article proposed the point that the sub-group is constantly changing by the evolution of the network, by dividing the community each time using the CNM algorithm. The CBTM were compared to the AB model, CBEN model and the actual IPv6IP-level topology, by contrasting the basic properties, the distribution of the degree, the network characteristic path length, the betweenness centrality and the power-law degree distribution of sub-cluster drawing the conclusion that the CBTM model can simulate the actual network topology very well.Third, this article researched the fractal characteristics of the IPv4router-level and IPv6IP-level topology. Due to the deep core level of IPv4routing-level and IPv6IP-level topology data, a k-level network coarse-grained method of the self-similarity fractal transform Internet was proposed, in order to obtained the sequence of the multi-scale network. And the qualitative analysis of the scaling analysis and the degree of correlation analysis and the quantitative analysis of fractal dimension show the boundary of the network fractal space is the junction of the middle k-level network and the high k-level network. The fractal characteristic of IPv6IP-level data is lower than the IPv4routing-level data, the reason maybe the development stage of the IPV6. The multi-scale network and the actual network have the same disassortativity. Fractal evolution in time is obviously related to the strength of the mutually exclusive between the high degree number nodes.Finally, the fractal characteristics of IPv4AS-level topology researched in this paper. The box covering method was introduced to carry out the self-similarity fractal transform the AS-level topology. And the conclusion that the multi-scale network of AS-level all exist the power-law and the fractal characteristic was draw by the calculation of the fractal dimension. The evolution analysis of the multi-scale network indicates that the average degree number has a gradually decreasing trend and the disassortativity of network did not change. The betweenness analysis of original network and the multi-scale network indicate that the importance of the node, in the coarse-grained network, is proportional to the size of the degree number of the node, and unrelated to size of coreness. The analysis of the closeness contrary indicates that the Average shortest path reduce in the coarse-grained network, and the closeness contrary of the node have not proportional to the coreness.