Phase locking induces scale-free topologies in networks of coupled oscillators

An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scale-free degree distribution in the original graph.