  Consider a random graph model with $n$ vertices where each vertex has a
vertex-type drawn from some discrete distribution. Suppose that the number of
arcs to be placed between each pair of vertex-types is known, and that each arc
is placed uniformly at random without replacement between one of the
vertex-pairs with matching types. In this paper, we will show that under
certain conditions this random graph model is equivalent to the well-studied
inhomogeneous random digraph model.
  We will use this equivalence in three applications. First, we will apply the
equivalence on some well known random graph models (the Erd\H{o}s-R\'enyi
model, the stochastic block model, and the Chung-Lu model) to showcase what
their equivalent counterparts with fixed arcs look like. Secondly, we will
extend this equivalence to a practical model for inferring cell-cell
interactions to showcase how theoretical knowledge about inhomogeneous random
digraphs can be transferred to a modeling context. Thirdly, we will show how
our model induces a natural fast algorithm to generate inhomogeneous random
digraphs.
