Topological properties of random wireless networks

Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs find many new applications and are being studied in their own right. In this paper we first provide a brief introduction to the issues of interest in random wireless networks. We then discuss some recent results for one-dimensional networks with the nodes distributed uniformly in (0, z). We then discuss some asymptotic results for networks in higher dimensions when the nodes are distributed in a finite volume. Finally we discuss some recent generalisations in considering non uniform transmission ranges and non uniform node distributions. An annotated bibliography of some of the recent literature is also provided.