  Many social and other networks exhibit stable size scaling relationships,
such that features such as mean degree or reciprocation rates change slowly or
are approximately constant as the number of vertices increases. Statistical
network models built on top of simple Bernoulli baseline (or reference)
measures often behave unrealistically in this respect, leading to the
development of sparse reference models that preserve features such as mean
degree scaling. In this paper, we generalize recent work on the
micro-foundations of such reference models to the case of sparse directed
graphs with non-vanishing reciprocity, providing a dynamic process
interpretation of the emergence of stable macroscopic behavior.
