From inhomogeneous random digraphs to random graphs with fixed arc counts

We consider a random digraph model where each vertex has a type drawn from some discrete distribution, and where a fixed number of arcs is placed randomly between vertices with given types. We provide conditions under which this model is equivalent to inhomogeneous random digraphs. We will apply this equivalence to well-known random digraphs including the Chung-Lu model, and extend it to a practical cell-cell interaction model.