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The Origin of Power Laws in Internet Topologies Revisited

By Qian Chen, Hyunseok Chang, Ramesh Govindan, Sugih Jamin, Scott J. Shenker and Walter Willinger

Abstract

In a recent paper, Faloutsos et al. [1] found that the inter Autonomous System (AS) topology exhibits a power-law vertex degree distribution. This result was quite unexpected in the networking community and stirred significant interest in exploring the possible causes of this phenomenon. The work of Barabasi and Albert [2] and its application to network topology generation in the work of Medina et al. [3] have explored a promising class of models that yield strict power-law vertex degree distributions. In this paper, we re-examine the BGP measurements that form the basis for the results reported in [1]. We find that by their very nature (i.e., being strictly BGP-based), the data provides a very incomplete picture of Internet connectivity at the AS level. The AS connectivity maps constructed from this data (the original maps) typically miss 20--50% or even more of the physical links in AS maps constructed using additional sources (the extended maps). Subsequently, we find that while the vertex degree distributions resulting from the extended maps are heavy-tailed, they deviate significantly from a strict power law. Finally, we show that available historical data does not support the connectivity-based dynamics assumed in [2]. Together, our results suggest that the Internet topology at the AS level may well have developed over time following a very different set of growth processes than those proposed in [2]

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