The Reliability Measure of Disconnected Network Based on Surviving Edges

Abstract

In wireless sensor networks, the disconnected network is an important and special one. Generally, the disconnected network is often characterized as a graph in graph theory. Suppose that edges fail independently of each other with equal probability and nodes are perfect. In this paper, a new reliability measure of disconnected network is proposed and defined as the probability that the edge-induced subgraph induced by surviving edges is connected. Different from traditional all-terminal reliability, this new reliability measure focuses on residual edge connectedness and is able to distinguish the reliability of two disconnected networks which are in the same class. Furthermore, the partial-star S is also proved to be uniformly best disconnected network under our proposed reliability measure in its class.