Construction of Directed Assortative Configuration Graphs

Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are independent. However, it is observed that many real-life networks are assortative, meaning that edges tend to connect low degree nodes with high degree nodes, or variations thereof. In this article we provide an explicit algorithm to construct directed assortative configuration graphs based on a given bi-degree distribution and an arbitrary pre-specified assortativity.