Loops structure of the Internet at the Autonomous System Level

Abstract

We present here a study of the clustering and loops in a graph of the Internet at the autonomous systems level. We show that, even if the whole structure is changing with time, the statistical distributions of loops of order 3, 4, and 5 remain stable during the evolution. Moreover, we will bring evidence that the Internet graphs show characteristic Markovian signatures, since the structure is very well described by two-point correlations between the degrees of the vertices. This indeed proves that the Internet belongs to a class of network in which the two-point correlation is sufficient to describe their whole local (and thus global) structure. Data are also compared to present Internet models.