Assortative mixing enhances the irreversible nature of explosive   synchronization in growing scale-free networks
  We discuss the behavior of large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and network's degrees. In particular, we show that the further presence of degree-degree correlation in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network's state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in growing scale-free networks. This latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization. 
I. Sendi\~na-Nadal, I. Leyva, A. Navas, J.A. Villacorta-Atienza, J.A.   Almendral, Z. Wang, S. Boccaletti
nlin.AO