Internet自治系统级拓扑复杂网络特征分析与验证

为深入理解和认清Internet复杂巨系统的不变特征和动态规律，分析研究Internet自治系统级拓扑的复杂网络特征，给出幂律分布和无标度条件的数学描述以及寻找两者之间的关系，分析小世界网络的两个重要特征，即较短平均路径长度和较大聚集系数，讨论匹配性问题和富人俱乐部现象，基于上述理论结果和BGP经验数据计算自治系统级拓扑的最大节点度、平均节点度、聚集系数和最大团数，发现自治系统级拓扑具有幂律分布、异配性以及富人俱乐部现象等复杂网络特征，得到幂指数、匹配系数以及富人俱乐部系数等重要特征参数。

Analysis and validation on complex network characteristics of Internet topology at autonomous system level

In order to understand deeply invariant characteristics and dynamic laws of the Internet complex giant system, the characteristics of the Internet topology at autonomous system level are analyzed.The mathematics definition of the pow- er-law distribution and the scale-free criterion, along with the relations between them are given.The main properties of the small-world network, i.e.the short average path length and the large clustering coefficient, are studied, and the assortativity and the rich-club phenomenon are discussed.Based the above theoretical results,the maximum node degree,the average node degree,the clustering coefficient and the maximum clique size of the topology of the Internet Autonomous System（AS） are calculated using experiential data collected from BGP protocol.The power-law distribution, disassortativity and rich-club phe- nomenon of the Internet AS are tested and verified,and the power exponent and assortativity coefficient and rich-club coefficient are obtained.