The Graph Structure of the Internet at the Autonomous Systems Level during Ten Years

We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features related to structure, connectivity and centrality changed over time. The analysis of these metrics provides topological and data traffic information and allows to clarify some assumptions about the models concerning the evolution of the Internet graph structure. We find that the size of the Internet roughly doubled. The overall trend of the average connectivity is an increase over time, while that of the shortest path length is a decrease over time. The internal core of the Internet is composed of a small fraction of big AS and is more stable and connected the external cores. A hierarchical organization emerges where a small fraction of big hubs are connected to many regions with high internal cohesiveness, poorly connected among them and containing AS with low and medium numbers of links. Centrality measurements indicate that the average number of shortest paths crossing an AS or containing a link between two of them decreased over time.