On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment

This paper investigates the connectivity of wireless multihop networks with uniformly randomly distributed nodes. We analyze the required transmission range that creates, for a given node density, an almost surely k-connected topology. Besides scenarios in which each node has the same range, we discuss inhomogeneous range assignments. Our results are of practical value for the task of setting parameters in network-level simulations of ad hoc networks and in the design of wireless sensor networks.