Number of h-cycles in the Internet at the Autonomous Systems level
We present here a study of the clustering and cycles present in the graph of Internet at the Autonomous Systems level. Even if the whole structure is changing with time, we present some evidence that the statistical distributions of cycles of order 3,4,5 remain stable during the evolution. This could suggest that cycles are among the characteristic motifs of the Internet. Furthermore, we compare data with the results obtained for growing network models aimed to reproduce the Internet evolution. Namely the fitness model and the Generalized Network Growth model. We are able to find some qualitative agreement with the experimental situation even if the actual number of loops seems to be larger in the data than in any proposed growing network models. The task to capture this feature of the Internet represent one of the challenges in the future Internet modeling.