Impact of square environment on the connectivity in finite ad hoc networks

This paper aims at studying some connectivity properties for random geometric graphs when they are constrained by the topological space in which they are embedded. More precisely, we focus our attention on limited square and rectangular environments. In order to analyse the impact of such environments on related graphs, we observe the evolution of mean degree. We propose an approach aiming at estimating the impact of the environment borders on the connectivity and we provide an analytical formula for computing the mean degree value depending on borders effects.