By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators synchronize and achieve phase coherence, and this process is not significantly affected by the level of connectivity of the network. If the probability that two oscillators are coupled is around the network connectivity threshold synchronization still occurs, although in a more attenuated way. If the size of the network is sufficiently large the oscillators have a phase transition.

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