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The term 'scale free' is a very unfortunate (and misleading) term that 
was spread based on the terminology choice of some individuals.  (Some 
people on this mailing list who know me are probably laughing their heads 
off and expecting me to go into one of my usual rants.  I'll spare 
you this time.)  It is used to refer to networks with degree distributions 
given by power laws (or, for real data, have power law tails) because a 
commonality of these sorts of scaling laws (which is different from 
scales, by the way, despite the similar terminology) one finds in fractal 
structures.  The thing is that networks with those degree distributions 
_can_ have scales, as discussed in gory detail by John Doyle and 
collaborators.  It's better to just state the power law aspect of it 
when one's network has that feature and not comment on whether or 
not there are scales unless one goes beyond the degree distribution.

One of Doyle's papers that discusses this is here:

I hope this helps.


> Dear all,
> Could you please give me some reference on Scale-free network?
> Why it is called scale-free? Please explain a bit to me.
> Thank you for your kind help.

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