I have been looking around for the definition of scale-free system I came up with, I had totally forgotten where I took it from. I think I kind of ripped it from this post and condensed it into a concise form.
During the presentation I gave a couple of days ago I was asked if this scale-free had anything to do with scale-free networks, which are networks that follow a power-law in degree distribution (a few vertexes with high degree [Hubs] and a lot of vertexes with low degree). These networks are used as a model for Internet, social networks and a lot of other things. They have some interesting properties that are kept no matter the scale (number of nodes) of the network, and thus they exhibit self-similarity, fractal structure and the like.
My answer is: no.
Or at least, when I say scale-free I mean that the scale is not a design parameter of the system. Or alternatively that the system’s design is free of scale, so you can run the system on 10 or 10^10 nodes without modification to the architecture. There might be some way so design a scale-free system using a power-law-distribution-of-something structure, but it is not the main point.