Research On Degree Correlation And Community Features Of Internet MacroscopicTopology

Nowadays modeling methods of Internet are able to construct more and more comprehensive topology, but can’t accurately reflect the community structure. Therefore, we proposed an Internet model with adjustable parameters. The statistic on Internet topological data indicates that the impact from high degree nodes is declining and Internet is becoming flat with multiple properties’ weakening. We found Internet community structure’s high modularity, coarse granularity and stable against scale via detailedly exploring toward connection discipline inner community and characteristic of nodes’dynamical behavior. A parameterized model was proposed and experiment proved it could embody general properties and community structure of Internet.Currently, the analysis of Internet topology and dynamical behavior usually adopt multiple angles and full-scale statistic. In order to avoid onesidedness, redundant complexity and unnecessary computation arise from over many measurements, this paper depicted the overall preferential connection using degree correlation coefficient with diversiform and sufficient real-world networks as analytical objects. The degree correlation coefficient was continuously changeable through Maximum Weighted Match (MWM) and Degree Preserve Rewire (DPR) algorithms, discussing the relationship between degree correlation coefficient and network topology based-on special topology such as regular and star. Those approaches were used to research the link between degree correlation coefficient and other topological features such as community and shortest path, after that, the degree correlation of Internet IP, router and AS were analyzed. In order to observer the degree correlation in different hierarchy, the Internet topology was k-core decomposed and degree correlation coefficient was computed for different k-cores. The computation result indicated that the disassortativity of Internet is weakening. In addition, different hierarchy of Internet has its own feature.The scale of Internet is large and various complex features interact to each other. For the purpose of avoiding interfering from over many measurements, the virus spreading based-on variation of degree correlation coefficient was simulated on the condition that degree distribution keeps unchanging. The result of qualitative analysis indicates that for assortative network, the spreading speed and stable infected proportion are lower but the threshold is also lower and this result is opposite on disassortative network. Quantitative analysis indicates there is evidence of phase transition in spreading with the increase of effective spreading rate. The community structure of Internet is clear and it is disassortative, which means the virus prevention on Internet should focus on isolation among sub communities and proliferation in large extent. Above research also imply that the virus prevention need synthetically consider the target and practical topology. Meanwhile, in order to improve the immunization both on assortative and disassorative network, we proposed one strategy aiming at target and acquaintance. The simulation result proved it is efficient to reduce spreading rate and infected proportion.With the high speed development of Internet, the amount of its topological data of IP and router is more numerous, which leads to some high complexity computation such as community dividing and simulation of spreading are becoming more and more difficult. Therefore, we proposed weighted community overlay network related conception and computation approach as measurements for different granularity of topology, thereby qualitatively analyzing each hierarchy and their correlation of weights. The statistics based-on large number of networks indicate that overlay network has stronger disassortativity and weaker community structure compared with original network. The quantitative analysis by community overlay network on IPV4and IPV6topologies shows Internet router-level topology has stronger community structure. Besides that, in the angle of qualitative, the community structure of IP-lever topology is more apparent than AS-level and router-levels, which can be proven via IPV6IP-level topology.