Analysis of the autonomous system network topology

Mapping the Internet is a major challenge for network researchers. It is the key to building a successful modeling tool able to generate realistic graphs for use in networking simulations. In this paper we provide a detailed analysis of the inter-domain topology of the Internet. The collected data and the resulting analysis began in November 1997 and cover a period of two and a half years. We give results concerning major topology properties (nodes and edges number, average degree and distance, routing policy, etc.) and main distributions (degree, distance, etc.). We also present many results about the trees of this network. The evolution of these properties is reviewed and major trends are highlighted. We propose some empirical laws that match this current evolution. Four new power-laws concerning the number of shortest paths between node pairs and the tree size distribution are provided with their detailed validation.