Sensor network localization attempts to determine the locations of a group of
sensors given the distances between some of them. The Semidefinite Programming
(SDP) relaxation of this problem is widely used to determine the locations of
the sensors. In this paper, we analyze and determine a number of conditions
that guarantee that the SDP relaxation is exact, i.e. gives the correct
solution. Our main contribution is twofold. We present the first non-asymptotic
bound on the connectivity range requirement of the sensors in order to ensure
the network is uniquely localizable.