Degree and connectivity of the Internet's scale-free topology
نویسندگان
چکیده
This paper theoretically and empirically studies the degree and connectivity of the Internet’s scale-free topology at an autonomous system (AS) level. The basic features of scale-free networks influence the normalization constant of degree distribution p(k). It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the kmin-degree (minimum degree) nodes and the kmax-degree (maximum degree) nodes, and the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. It finds that the average degree is larger for a smaller power-law exponent λ and a 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 Internet AS-level topology. In addition, it is revealed that the increase rate of the average degree or the ratio of the kmin-degree nodes has power-law decay with the increase of kmin. The ratio of the kmax-degree nodes has a power-law decay with the increase of kmax, and
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