Category Archives: fractals

The root of the power law religion

New draft paper by me. Update: Published here. The abstract:

A ‘power law’ refers specifically to a statistical relationship between quantities, such that a change in one quantity has a proportional change in another. One property of this law is scale invariance, otherwise known as ‘scale-free,’ meaning the same proportion repeats at every scale in a self-similar pattern. Mathematical fractals are an example of such a power law. Power laws are taken as universal and have been applied to any and all phenomena to prove the universality of this law.

However, a recent study (Broido and Clauset, 2019) claims that “scale free networks are rare.” They conducted an extensive review of one thousand social, biological, technological and information networks using state of the art statistical methods and concluded what the title of their article states. To the contrary, “log-normal distributions fit the data as well or better than power laws.” And that scale-free structure is “not an empirically universal pattern.” Hence it should not be used to model and analyze real world structures.

scale-free networks are rare

I linked to this article for our recent discussion of brain networks. The abstract is below.

“Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws.”