Social networks can provide useful information to enhance mobile cyber-physical applications. With advanced sensor and powerful mobile Internet device technologies, future social networking is likely to be cyber-physical, combining social behaviors and human interactions with computational and physical processes. This paper addresses the problem of analyzing and extracting useful properties from a social cyber-physical network. In particular, we present a graph-based approach to automatically identifying essential nodes that hold the network together called key breakers. Knowing key breakers can help us contain spread of diseases, computer viruses, and undesirable communication or security breaches in the network. The paper describes the approach and provides illustrations, empirical evaluation and a comparative study with existing techniques.