Degree and connectivity of the Internet's scalefree topology
Abstract
This paper theoretically and empirically studies the degree and connectivity of the Internet's scalefree topology at an autonomous system (AS) level. The basic features of scalefree networks influence the normalization constant of degree distribution p(k). It develops a new mathematic model for describing the powerlaw relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the k_{min}degree (minimum degree) nodes and the k_{max}degree (maximum degree) nodes, and the fraction of the degrees (or links) in the hands of the richer (top bestconnected) nodes. It finds that the average degree is larger for a smaller powerlaw exponent λ and a larger minimum or maximum degree. The ratio of the k_{min}degree nodes is larger for larger λ and smaller k_{min} or k_{max}. The ratio of the k_{max}degree ones is larger for smaller λ and k_{max} or larger k_{min}. The richer nodes hold most of the total degrees of Internet ASlevel topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the k_{min}degree nodes has powerlaw decay with the increase of k_{min}. The ratio of the k_{max}degree nodes has a powerlaw decay with the increase of k_{max}, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the ‘73/27 rule’). Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet ASlevel topology.
 Publication:

Chinese Physics B
 Pub Date:
 April 2011
 DOI:
 10.1088/16741056/20/4/048902
 arXiv:
 arXiv:1101.4285
 Bibcode:
 2011ChPhB..20d8902Z
 Keywords:

 Computer Science  Networking and Internet Architecture;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society
 EPrint:
 22 pages, 8 figures