  We introduce, and analyze, three measures for degree-degree dependencies,
also called degree assortativity, in directed random graphs, based on
Spearman's rho and Kendall's tau. We proof statistical consistency of these
measures in general random graphs and show that the directed configuration
model can serve as a null model for our degree-degree dependency measures.
Based on these results we argue that the measures we introduce should be
preferred over Pearson's correlation coefficients, when studying degree-degree
dependencies, since the latter has several issues in the case of large networks
with scale-free degree distributions.
