I am working on a directed graph, where in and out degree distributions are extrimely different: while the in-degree is for sure following a power-law, the out degree is not. Also, the in degree is a huge portion of the total one. I have checked the power-law hypothesis as suggested here, and got a p-value of 0.88 which should mean the whole degree distribution is following nicely a power-law. I also extimated the gamma parameter, and got that it should be around 2.6, suggesting that the regime my network is following is an ultra-small world. Only after doing this and viewing a significant difference between the theorical and actual average distance (2.5 vs 8), I thought that it could be wrong defining the network as scale free since the out-degree is not following a power-law distribution at all. Here you can see the distributions of in, out and total degree: 
Basically, I think the whole analysis I have done on this network, calling it scale free and supposing it to be like that, is garbage because of this. I would be extremely interested in reading others opionions and am hoping for someone to write me that I am wrong and that this is in fact a scale free network. Thank you very much.
