K-Shell Decomposition of AS Level Multigraphs

Abstract

The Internet is one of the immense human-engineered systems and understanding of the topology can be helpful for network engineers and researchers. Categorization of Autonomous Systems (ASes) plays an essential role in understanding the structure and evolution of the Internet. However, the traditional categorization exhibits variation in different studies, contains ambiguity, involves subjectiveness, and sometimes does not match the reality. A better approach to classify ASes is defining the AS level topology maps as graphs and taking advantage of the graph properties through k-shell decomposition. However, the proposed solutions neither capture the parallel connections nor incorporate the varying business relations among the ASes. Abstracting ASes without any internal structure is an oversimplification since the ASes in the Internet span over various geographic regions and often cover the same regions in part or whole. In this work, we introduce k-shell decomposition on AS level multigraphs and comparison with AS level graphs. The decomposition is based on pruning the graphs according to the nodes’ connectivity pattern to generate a layered structure of the Internet. In our experiments, we analyze the structure of the shells and the connectivity structure of the Internet. Additionally, we compare top-20 ASes to understand the central core of the Internet. Our comparative results help us to understand the structure of the Internet better.