In complex networks, the degrees of adjacent nodes may often appear dependent-which
presents a modelling challenge. We present a working framework for studying networks
with an arbitrary joint distribution for the degrees of adjacent nodes by showing
that such networks are a special case of edge-coloured random graphs. We use this
mapping to study bond percolation in networks with assortative mixing and show that,
unlike in networks with independent degrees, the sizes of connected components may
feature unexpected sensitivity to perturbations in the degree distribution. The results
also indicate that degree-degree dependencies may feature a vanishing percolation
threshold even when the second moment of the degree distribution is finite. These
results may be used to design artificial networks that efficiently withstand link
failures and indicate the possibility of super spreading in networks without clearly
distinct hubs.
