The generation of random directed networks with prescribed 1-node and 2-node degree correlations

The generation of random networks is a very common problem in complex network research. In this paper, we have studied the correlation nature of several real networks and found that, typically, a large number of links are deterministic, i.e. they cannot be randomized. This finding permits fast generation of ensembles of maximally random networks with prescribed 1-node and 2-node degree correlations. When the introduction of self-loops or multiple-links are not desired, random network generation methods typically reach blocked states. Here, a mechanism is proposed, the 'force-and-drop' method, to overcome such states. Our algorithm can be easily simplified for undirected graphs and reduced to account for any subclass of 2-node degree correlations.