k-core decomposition: a tool for the analysis of large scale Internet graphs
Résumé
We use the $k$-core decomposition, based on a recursive pruning of the least connected vertices, to study large scale Internet graphs at the Autonomous System level. This approach allows the characterization of progressively central cores of networks, conveniently uncovering hierarchical and structural properties. Internet maps show the noticeable property of having all $k$-cores consisting of a single connected component with invariant statistical properties (degree distribution, correlation spectrum etc.). This feature suggests that the Internet is organized in a defined hierarchy of connected subgraphs of increasing centrality with self-similar properties. The $k$-core decomposition provides also an interesting tool to follow the temporal evolution of Internet maps and test the stability and reliability of different mapping strategies.