# Is there a generative network model for arbitrary distributions that guarantees an edge count?

So what I am trying to do is rewire a random directed graph (specifically a boolean network) so the out-degree distribution is scale-free. However I need a generative model that will allow me to specify the amount of total edges. This is because the random boolean networks I'm using have a constant in-degree.

So I found the generative model here which is the configuration model. This involves computing a finite version of the distribution's PMF and then randomly choosing (weighted by distribution) a degree for each node. However there is no way of specifying what the total edge count should be. How could I go about doing this? Is there a rewiring type of generative model for this? It would be great if the answer works for any arbitrary distribution.

• What does it mean for the out-degree distribution to be "scale-free"? – Jair Taylor Mar 22 at 1:02
• The out-degree should have the distribution $P(k) \sim k^{-\gamma}$. – Jonathan Mar 22 at 1:40