The location of sensor nodes in wireless sensor networks plays an important role in most applications. In this paper, we address the localization problem by characterizing some sufficient conditions such that technical convenience for the collection of local information used for network localization can be enabled. The main contribution of this paper is as follows. Some latest research results on the graph rigidity theory are introduced and incorporated, and a feasible node localization scheme is presented. More specifically, a tree structure termed BN-tree is introduced to construct a localizable collaborative body. Especially, the localizable collaborative body can be constructed dynamically with the variety of the network topology. Simulation results, which show that the quality of localization is well bounded by the range of communication, are also provided to validate the proposed algorithm.