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The proliferation of wireless and mobile devices has fostered the demand of context-aware applications, in which location is often viewed as one of the most significant contexts. Classically, trilateration is widely employed for testing network localizability; even in many cases, it wrongly recognizes a localizable graph as nonlocalizable. In this study, we analyze the limitation of trilateration-based approaches and propose a novel approach that inherits the simplicity and efficiency of trilateration and, at the same time, improves the performance by identifying more localizable nodes. We prove the correctness and optimality of this design by showing that it is able to locally recognize all one-hop localizable nodes. To validate this approach, a prototype system with 60 wireless sensors is deployed. Intensive and large-scale simulations are further conducted to evaluate the scalability and efficiency of our design.