A Social Network Approach for the Ranking of the Autonomous Systems of the Internet

The worldwide scale transit of information flows in the Internet is governed by trade agreements between autonomous systems; these agreements are translated into routing policies by the Border Gateway Protocol (BGP). The negotiation of these trade agreements implicitly relies on a hierarchy of the autonomous systems and the relative position of two systems leads to an agreement of the customer-provider type (one of the systems, the provider, is ranked higher than the other, the client, and the client pays the provider for the transit of information flows) or to a no cost agreement of the "peering" type (two service providers that agree to exchange traffic between their respective customers) when both systems consider their rankings to be equivalent. In spite of its importance, there is no official hierarchy of the Internet (the commercial clauses of the agreements between autonomous systems are not necessarily public, it is usually a bilateral arrangement) nor a consensus on the way of establishing such a hierarchy. We propose a simple heuristics inspired of the concept of "spectral centrality" borrowed from the social networks analysis to analyze the relative positions of the autonomous systems of the Internet starting from their connectivity information only.