  Analysis of degree-degree dependencies in complex networks, and their impact
on processes on networks requires null models, i.e. models that generate
uncorrelated scale-free networks. Most models to date however show structural
negative dependencies, caused by finite size effects. We analyze the behavior
of these structural negative degree-degree dependencies, using rank based
correlation measures, in the directed Erased Configuration Model. We obtain
expressions for the scaling as a function of the exponents of the
distributions. Moreover, we show that this scaling undergoes a phase
transition, where one region exhibits scaling related to the natural cut-off of
the network while another region has scaling similar to the structural cut-off
for uncorrelated networks. By establishing the speed of convergence of these
structural dependencies we are able to asses statistical significance of
degree-degree dependencies on finite complex networks when compared to networks
generated by the directed Erased Configuration Model.
