  In the new field of financial systemic risk, the network of interbank
counterparty relationships can be described as a directed random graph. In
"cascade models" of systemic risk, this "skeleton" acts as the medium through
which financial contagion is propagated. It has been observed in real networks
that such counterparty relationships exhibit negative assortativity, meaning
that a bank's counterparties are more likely to have unlike characteristics.
This paper introduces and studies a general class of random graphs called the
assortative configuration model, parameterized by an arbitrary node-type
distribution P and edge-type distribution Q. The first main result is a law of
large numbers that says the empirical edge-type distributions converge in
probability to Q. The second main result is a formula for the large N
asymptotic probability distribution of general graphical objects called
"configurations". This formula exhibits a key property called "locally
tree-like" that in simpler models is known to imply strong results of
percolation theory on the size of large connected clusters. Thus this paper
provides the essential foundations needed to prove rigorous percolation bounds
and cascade mappings in assortative networks.
