Degree distribution and hop count in wireless ad hoc networks

Abstract—This article is a contribution to mathematical mod-eling and better understanding of fundamental properties of wireless ad-hoc networks. Our focus in this article is on the degree distribution and hopcount in these networks. The results presented here are useful in the study of connectivity and estimation of the capacity in ad-hoc networks. We model a wireless ad-hoc network as an undirected geometric random graph. For the calculation of the link probability between nodes we have suggested to use a realistic radio model; the so-called log-normal shadowing model. Through a combination of mathematical modeling and simulations we have shown that the degree distribution in wireless ad-hoc networks is binomial for low values of the mean degree. Further, we have investigated the hopcount and have shown that the hopcount in wireless ad-hoc networks can vary between the expected values for lattice networks and random graphs, depending on radio propagation conditions