Abstract
It is well known that dynamical processes on complex networks are influenced by the degree correlations. A common way to take these into account in a mean-field approach is to consider the function k_{nn}(k) (average nearest neighbors degree). We re-examine the standard choices of knn for scale-free networks and a new family of functions which is independent from the simple ansatz k_{nn} ~ ยต k^a but still displays a remarkable scale invariance. A rewiring procedure is then used to explicitely construct synthetic networks using the full correlation P(h|k) from which k_{nn} is derived. We consistently find that the k_{nn} functions of concrete synthetic networks deviate from ideal assortativity or disassortativity at large k. The consequences of this deviation on a diffusion process (the network Bass diffusion and its peak time) are numerically computed and discussed for some low-dimensional samples. Finally, we check that although the k_{nn} functions of the new family have an asymptotic behavior for large networks different from previous estimates, they satisfy the general criterium for the absence of an epidemic threshold.