Connectivity properties of large-scale sensor networks

In wireless sensor networks, both nodes and links are prone to failures. In this paper we study connectivity properties of large-scale wireless sensor networks and discuss their implicit effect on routing algorithms and network reliability. We assume a network model of n sensors which are distributed randomly over a field based on a given distribution function. The sensors may be unreliable with a probability distribution, which possibly depends on n and the location of sensors. Two active sensor nodes are connected with probability p _e (n) if they are within communication range of each other. We prove a general result relating unreliable sensor networks to reliable networks. We investigate different graph theoretic properties of sensor networks such as k-connectivity and the existence of the giant component. While connectivity (i.e. k = 1) insures that all nodes can communicate with each other, k-connectivity for k > 1 is required for multi-path routing. We analyze the average shortest path of the k paths from a node in the sensing field back to a base station. It is found that the lengths of these multiple paths in a k-connected network are all close to the shortest path. These results are shown through graph theoretical derivations and are also verified through simulations.