k-dense communities in the internet AS-level topology

Extracting a set of well connected subgraphs as communities from the Internet Autonomous System (AS) level topology graph is crucially important for a better understanding of the network structure and for designing new protocols. A huge number of community extraction methods have been proposed in the literature. In this paper we apply the k-dense algorithm as it represents a very interesting compromise between computational efficiency and precision. The paper provides two innovative contributions. The first is the application of the k-dense method to the Internet AS-level topology graph - obtained from the CAIDA, DIMES and IRL datasets - to identify well-connected communities and to analyze how these are connected to the rest of the graph. The second contribution relates to the study of the most well-connected communities with the support of two additional datasets: a geographical dataset (which lists, for each AS, the countries in which it has at least one geographical location) and the Internet eXchange Point dataset (which maintains, for each IXP, its geographical position and the list of its participants). We found that the k-max-dense community holds a central position in the Internet AS-level topology graph structure since its 101 ASes (less than the 0.3% of Internet ASes) are involved in more than 39% of all Internet connections. We also found that those ASes are connected to at least one IXP and have at least one geographical location in Europe (only 70.3% of them have at least one additional geographical location outside Europe).