Degree mixing and the enhancement of synchronization in complex weighted networks.

Real networks often consist of local units interacting with each other by means of heterogeneous connections. In many cases, furthermore, such networks feature degree mixing properties, i.e., the tendency of nodes with high degree (with low degree) to connect with connectivity peers (with highly connected nodes). Such degree-degree correlations may have an important influence in the spreading of information or infectious agents on a network. We explore the role played by these correlations for the synchronization of networks of coupled dynamical systems. Using a stochastic optimization technique, we find that the value of degree mixing providing optimal conditions for synchronization depends on the weighted coupling scheme. We also show that a minimization of the assortative coefficient may induce a strong destabilization of the synchronous state. We illustrate our findings for weighted networks with scale free and random topologies.