In most realistic networked systems where synchronization is relevant, synchronization may also be related to pathological activities such as epileptic seizures and strong Parkinson disease in neural networks, to extinction in ecology. In fact, various levels of synchronization are needed to avoid pathological activities and enable a system to have flexibility and robustness. Recently, it has been observed the synchronization may arise between well-connected nodes (hubs) while less connected nodes do not synchronize. We discuss a probabilistic approach towards the explanation of this phenomenon in the limit networks of large random networks.