Accirate subgraph probabilities in a Random Geometric Graph and application to cooperative multihop ad-hoc networks

In this paper, we propose a new model to determine subgraph probabilities in a Random Geometric Graph(RGG). A subgraph in a RGG can be used to model various scenarios involving a given number of nodes in a multihop ad hoc network. We determine the probabilities for the two essential cases of complete subgraphs with three and four vertices, respectively, which have not yet been addressed correctly in the literature. Our theoretical results are confirmed by simulation and thus represent a significant step towards the quantitative analysis of complex scenarios, such as cooperative communications, in multi hop ad-hoc networks.