Scale-Free Networks Are Rare

From the abstract:

A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree k follows a power law [...] Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain.

I was involved in that kind of research in the 1990s and it was clear to me at the time that the people doing that kind of research didn't even know what an "estimator" was and didn't care to know.