I have a real world network where I've plotted the degree distribution. If the network was formed from a Barabási–Albert model, the degree distribution should be roughly a power law of the form $P(k)=k^{-3}$. Instead the distribution looks like:
The peaks of in the tail of the graph are understandable from a physical perspective (in that, I expect a set of abnormally well-connected nodes).
Concerning the rest of the distribution however, I'm perplexed. Are there any graph models that will create a distribution with this shape?