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.
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We demonstrate the strength of our embedding with two applications: selecting 
the closest server and building an application level multicast tree.