Internet分形特征研究

采用k-核分解算法对Internet分形特征进行研究.对高核区间和低核区间拟合结果的差异进行分析,提出Internet分形特征与其结构的层次性存在关联的猜想.随后,从删边数、删边比例和子网分布三个角度对k-核分解过程进行观察,确定Internet核心层与边缘层的分割边界,并利用骨架树理论研究Internet的层次分形特征.最后,从度分布指数、同配系数和结构熵等常见统计角度对Internet部分与整体,以及部分与部分之间的关系进行观察.观察表明,在以上统计角度,Internet边缘子网可以表征网络整体.

Research on Fractal Property of Internet

The k-core decomposition algorithm was applied to the study of the Internet fractal property. During the study， the difference of fitting results between high-core region and low-core region was analyzed， and a conjecture was proposed that Internet fractal is related to its hierarchical structure. Subsequently， the k-core decomposition process was observed from three aspects: the number and ratio of deleted edges， and subnets distribution. A partition boundary was found which was useful to distinguish core and periphery， then the Internet fractal hierarchy was studied with the help of the skeleton theory. Finally， relations between part and whole， part and part were observed from degree distribution exponent， assortativity coefficient， and entropy. The observations show that the subnets in the Internet edge can characterize the network from the statistics above.