Node density, connectivity and the percolation threshold

The purpose of this study is to document a background analysis that has been performed in order to set the parameters for simulation studies used by the author in scholarly published articles. The background information has not been in the published material due to space restrictions, but it may be of interest for a wider audience in the field. When evaluating routing protocols and other protocols in mobile ad hoc networks (MANETs) and delay-tolerant networks (DTNs) one factor influencing the result is the node density. To understand what a certain node density means in term of connectivity properties we have by simulation evaluated how well connected a system of randomly placed nodes are for different node densities and network sizes. We have compared these densities to the percolation threshold to understand how much we need to increase the density over the percolation threshold to, with high probability, have a fully connected system provided that the number of nodes are finite. The percolation threshold is the node density above which it is almost surely guaranteed that the largest connected component in an infinite system is of infinite size. Finally we provide a survey of node densities used in some recent MANET and DTN studies