大型ISP网络拓扑多点测量及其特征分析实例

深入了解Internet拓扑的结构性质有利于更好地设计和发展Internet.由于Internet规模巨大,以及获得完整的路由器级Internet拓扑方面的困难,目前无法研究整个路由器级Internet拓扑.因此,分别研究每个国家级或跨国因特网服务供应商(Internet service provider,简称ISP)网络拓扑结构成为了解Internet拓扑特征的一种可选方法.以中国教育科研网为例,简要描述了多点测量其路由器级拓扑结构的测量结果.分析了该实例拓扑图的节点度分布特征、较大特征值的有关性质以及谱密度分布特征.分析了该实例拓扑图的无符号拉普拉斯谱(SLS)、规格化拉普拉斯谱(NLS)以及群集系数等度量特征.分析结果表明,大型ISP拓扑确实具有某些幂律特征;不同于自治系统级拓扑的情形,对ISP拓扑的节点度补累积分布来说,幂律分布未必拟合得最好;ISP拓扑是一种无标度图,但不符合Barabasi-Albert(BA)生长模型;SLS和NLS具有区分不同的路由器级拓扑结构的能力;Internet路由器级拓扑的发展可能遵循一种不同于BA模型的生长过程.

An Example of Analyzing the Characteristics of a Large Scale ISP Topology Measured from Multiple Vantage Points

A detailed understanding of the structural properties of Internet topology will benefit the further design and development of the Internet. It seems infeasible to study the whole Internet at router level due to its extremely large size and the difficulty in obtaining a whole topology at this level. Studying each national or continental Internet service provider (ISP) topology individually becomes an alternative method for this goal. In this paper, the measured China Education and Research Network topology, a nationwide ISP topology, is basically taken as an example. The results of mapping the topology from multiple vantage points are briefly presented. The properties of the degree distribution, large eigenvalues, and the spectral density of the measured topology graphs are analyzed. The characteristics of the signless Laplacian spectra (SLS), the normalized Laplacian spectra (NLS), and the clustering coefficients of the measured graphs are also presented. The results suggest that some power laws indeed hold in some large-scale ISP topologies; in contrast to the case of autonomous system level topologies, the power law fit is not the best choice for some ISP topologies in terms of the complementary cumulative distribution function of the degree; some real ISP topologies are a kind of scale-free graphs which are not consistent with the Barabási-Albert (BA) growth model; router level topologies are distinguishable in terms of the SLS or the NLS; router level Internet topology may have developed over time following a different set of growth processes from those of the BA model.