Loops structure of the Internet at the Autonomous System Level

Abstract

We present here a study of the clustering and cycles in the graph of 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 3,4,5 remain stable during the evolution. Moreover we will bring evidence that the Internet graphs show characteristic Markovian signatures, since the loops structure is very well described by the two point correlations between the connectivities of the nodes. This represent another essential characteristic of this evolving graph. To capture this feature of the Internet represent one of the challenges in the future Internet modeling.