Internet拓扑中连接率的研究

近年来，一些学者对互联网的拓扑结构进行了深入的研究，发现在互联网拓扑中存在幂律(Power-Law)，其相关系数最高可达到99％。本文在Internet的每个子图上引进连接率的概念以刻划该子图中结点相互连接的程度，然后对Internet中的结点按其连接边数的多少由多到少进行排序，通过逼近实验和理论推导两个方面的工作，发现在Internet前r个结点的诱导子图上的连接率作为子图上结点数r的函数满足幂律，其相关系数超过99．3％。这一结果是目前在Internet中所发现的吻合得相当好的幂律，期望它可推动Internet拓扑结构的整体性质的深入研究。

Research on the Connectivity Coefficients of Internet Topology

In recent years, some researchers have made profound study on the Internet topology. It was found that there exist several power laws in the Internet, and the correlation coefficients are between 96% and 99%. In this paper, the concept of connectivity coefficient in sub-graphs of the Internet is introduced, then the nodes of the Internet is reordered according to their degrees from large to small, and it is found, through both empirical study and theoretical argument, that the connectivity coefficient of the sub-graph induced by the preceding r nodes, as a function of r, also satisfies power law, and the correlation coefficient will exceed 99 3%. This result is the most exact power law found in the Internet up to now, it is helpful, as expected, for the understanding of the whole structure of the Internet.