So, what I'm trying to do is to rewire a randomly directed graph (especially a Boolean lattice) so that the lower degree distribution is scaleless. However, I need a generative model that allows me to specify $ gamma $ in $ P (k) sim k ^ {- gamma} $.

I imagine that there is a certain ratio of rewiring $ n / m $ (rewiring $ n $ out of $ m $ total edges) with preferential attachment (proportional to the existing outer degree) that will produce this result on average. But I do not know how to convert $ gamma $ in this report.

I would like to know if such a generative model exists. What would be even better is to learn how to arrive at such a model, whether it exists or not.