Our research focusses on the problem of finding nearby peers in the Internet. We focus on one particular approach, Beacon Triangulation that is widely used to solve the peer-finding problem. Beacon Triangulation is based on relative distances of nodes to some special nodes called beacons. The scheme gives an error when a new node that wishes to join the network has the same relative distance to two or more nodes. One of the reasons for the error is that two or more nodes have the same distance vectors. As a part of our research work, we derive the conditions to ensure the uniqueness of distance vectors in any network given the shortest path distribution of nodes in that network. We verify our analytical results for G(n, p) graphs and the Internet. We also derive other conditions under which the error in the Beacon Triangulation scheme reduces to zero. We compare the Beacon Triangulation scheme to another well-known distance estimation scheme known as Global Network Positioning (GNP).