Finding a dense-core in jellyfish graphs

The connectivity of the Internet crucially depends on the relationships between thousands of Autonomous Systems (ASes) that exchange routing information using the Border Gateway Protocol (BGP). These relationships can be modeled as a graph, called the AS-graph, in which the vertices model the ASes, and the edges model the peering arrangements between the ASes. Based on topological studies, it is widely believed that the Internet graph contains a central dense-core: Informally, this is a small set of high-degree, tightly interconnected ASes that participate in a large fraction of end-to-end routes. Finding this densecore is a very important practical task when analyzing the Internet's topology. In this work we introduce a randomized sublinear algorithm that finds a densecore of the AS-graph. We mathematically prove the correctness of our algorithm, bound the density of the core it returns, and analyze its running time. We also implemented our algorithm and tested it on real AS-graph data. Our results show that the core discovered by our algorithm is nearly identical to the cores found by existing algorithms - at a fraction of the running time.