On Power-Law Relationships of the Internet Topology

This paper addresses the need for accurate models of the Internet topology, for simulation purposes as well as for analyzing and optimizing protocols. Topology can be studied at the intra-domain or inter-domain level using metrics such as node out-degree and inter-node distance. Power-laws have previously been used to describe network traffic but not network topology; probabilistic distance-based models have been very popular for this purpose. The authors aim to identify useful relationships between graph parameters, choosing parameters that can be captured with one number. For example, some chosen parameters are the rank exponent, the out-degree exponent and the hop-plot exponent.

One naturally wonders how such strict relationships emerge in a chaotic network of both cooperative and antagonistic forces such as the modern Internet. The authors anticipate and respond to this quandary with a discussion of the dynamic equilibrium reached in the disorder of the Internet. Several arguments are made in favor of further exploring such power-laws, such as the ubiquity of self-similarity and chaos. I really enjoyed this read and agree that this could be very important for network research going forward. The emergence of these power-laws is reminiscent of Gaussian and Poisson distributions describing various environments in communication and biology - we all know how these mathematical models have guided research in those disciplines.