  In this paper we study the synchronization properties of random geometric
graphs. We show that the onset of synchronization takes place roughly at the
same value of the order parameter that a random graph with the same size and
average connectivity. However, the dependence of the order parameter with the
coupling strength indicates that the fully synchronized state is more easily
attained in random graphs. We next focus on the complete synchronized state and
show that this state is less stable for random geometric graphs than for other
kinds of complex networks. Finally, a rewiring mechanism is proposed as a way
to improve the stability of the fully synchronized state as well as to lower
the value of the coupling strength at which it is achieved. Our work has
important implications for the synchronization of wireless networks, and should
provide valuable insights for the development and deployment of more efficient
and robust distributed synchronization protocols for these systems.
