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arXiv 1101.4285cs.NIcs.SIphysics.soc-ph
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Internet无标度拓扑的度和连通性

Degree and connectivity of the Internet's scale-free topology

Lianming Zhang, Xiaoheng Deng, Jianping Yu, Xiangsheng Wu

摘要:

在本文中,我们从理论和实证上研究了互联网的自治系统(AS)水平上的无标度拓扑结构的程度和连通性。无标度网络的基本特征对度分布p(k)的归一化常数有影响。建立了一个互联网无标度拓扑的数学模型。在这个模型上,我们从理论上得到了平均度、kmin度(最小度)节点和kmax度(最大度)节点的比率、最富有(最佳连通)节点手中的度(或链接)的分数的公式。我们发现幂律指数λ越小,最小度或最大度越大,平均度越大。对于较大的λ和较小的kmin或kmax,kmin度节点的比率较大。对于较小的λ和kmax或较大的kmin,kmax度的比率较大。较丰富的节点拥有AS级Internet拓扑的大部分总度。此外,我们还揭示了kmin度节点的比例或平均度的增长率随kmin的增加呈幂律衰减。随着kmax的增加,kmax度节点的比例呈幂律衰减,并且在较富裕的27%节点手中的度的分数约为73%(“73/27规则”)。最后,基于BGP的经验数据,对该方法和其他方法的平均度、比率和分数进行了实证计算,结果表明,该方法对AS级的Internet拓扑结构是严格有效的。

英文摘要:

In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization constant of the degree distribution p(k). We develop a mathematics model of the Internet's scale-free topology. On this model we theoretically get the formulas of the average degree, the ratios of the kmin-degree (minimum degree) nodes and the kmax-degree (maximum degree) nodes, the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. We find the average degree is larger for smaller power-law exponent λ and larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger λ and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller λ and kmax or larger kmin. The richer nodes hold most of the total degrees of the AS-level Internet topology. In addition, we reveal the ratio of the kmin-degree nodes or the rate of the increase of the average degree has power-law decay with the increase of the kmin. The ratio of the kmax-degree nodes has power-law decay with the increase of the kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). At last, we empirically calculate, based on empirical data extracted from BGP, the average degree and the ratio and fraction using our method and other methods, and find that our method is rigorous and effective for the AS-level Internet topology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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