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The use of degree-degree correlations to model realistic networks which arecharacterized by their Pearson's coefficient, has become widespread. Howeverthe effect on how different correlation algorithms produce different results onprocesses on top of them, has not yet been discussed. In this letter, usingdifferent correlation algorithms to generate assortative networks, we show thatfor very assortative networks the behavior of the main observables inpercolation processes depends on the algorithm used to build the network. Thedifferent alghoritms used here introduce different inner structures that aremissed in Pearson's coefficient. We explain the different behaviors through ageneralization of Pearson's coefficient that allows to study the correlationsat chemical distances l from a root node. We apply our findings to realnetworks.

Effect of degree correlations above the first shell on the percolation transition