On the curvature of the Internet and its usage for overlay construction and distance estimation

It was noted in recent years that the Internet structure resembles a star with a highly connected core and long stretched tendrils. In this work we present a new quantity, the Internet geometric curvature, that captures the above observation by a single number. We embed the Internet distance metric in a hyperbolic space with an optimal curvature and achieve an accuracy better than achieved before for the Euclidean space. This proves our hypothesis regarding the internet curvature. We demonstrate the strength of our embedding with two applications: selecting the closest server and building an application level multicast tree.