Random networks tossing biased coins

In statistical mechanical investigations of complex networks, it is useful to employ random graph ensembles as null models to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with asymptotically, scale-free out-degree and compact in-degree. Entries in each row of the adjacency matrix are set to 0 or 1 according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n approximately 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs. The technique is easily generalizable to different kinds of graphs.