Loops structure of the Internet at the Autonomous System Level

TL;DR

This paper analyzes the Internet's Autonomous System graph, revealing stable loop distributions over time and Markovian properties, highlighting key structural features for future modeling.

Contribution

It uncovers the stable distributions of small loops and demonstrates the Markovian nature of the Internet's AS-level graph structure.

Findings

Loop distributions of order 3, 4, 5 are stable over time

Internet graphs exhibit Markovian signatures

Two-point correlations describe loop structures effectively

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.