  In this work we introduce Dynamic Random Geometric Graphs as a basic rough
model for mobile wireless sensor networks, where communication distances are
set to the known threshold for connectivity of static random geometric graphs.
We provide precise asymptotic results for the expected length of the
connectivity and disconnectivity periods of the network. We believe the formal
tools developed in this work could be of use in future studies in more concrete
settings. In addition, for static random geometric graphs at the threshold for
connectivity, we provide asymptotic expressions on the probability of existence
of components according to their sizes.
