More precisely, researchers from University of Colorado, Boulder, argue that Scale-free networks are rare(1):
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, decaying like kα, often with 2 < α < 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. We test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. 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.
Oh, poor Albert-László Barabási!
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(1) Broido, Anna D., and Aaron Clauset. 2018. ‘Scale-Free Networks Are Rare’, January. https://arxiv.org/abs/1801.03400.
Mind the Post 
Please excuse my ignorance, but are the following typos?
“We t the power-law model…”
“Across domains, we nd that scale-free networks…”
Thank you!!
Very good! But also to be expected
As you quote: “The daunting reality of complexity research is that the problems it tackles are so diverse that no single theory can satisfy all needs”
By the way, do you know this course?
https://www.coursera.org/learn/social-economic-networks
or even
https://www.complexityexplorer.org/courses/85-fractals-and-scaling
I liked them
I shall try to have a look at Barabasi’s
As usually, you are right. In fact (tittle notwithstanding) what I find surprising is that there are quite a few number of networks that seem to fit in the model…
Yes… remember that when you have a hammer all things resemble a nail. Of course, the scale free models are useful, but it does not mean that an essentially heuristic approach can be applicable everywhere.
A lot depends on how we choose the data to be fitted.
See for example: Clauset, Aaron, Cosma Rohilla Shalizi, and Mark EJ Newman. “Power-law distributions in empirical data.” (https://arxiv.org/abs/0706.1062)