Distribution of k -connectivity in the secure wireless sensor network

In this paper we are considering a wireless sensor network with secure communication. k -connectivity is one of the most desirable features in a wireless sensor network (WSN). It allows messages to be routed through one (or more) of at least k disjoint paths. This ensure that if some nodes along one of the paths fail, or compromised, the other paths can still be used for sending data. We derive mathematical expression for the probability of a wireless sensor network being k -connected. Also calculated the expected secure k -connectivity. We have given simulation results too through which we are able to show that as the size of the network increases, direct communication between the node decreases but the muti-hop communication increases.