There is no such thing as a scale free network

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.

 

5 comments

  1. Please excuse my ignorance, but are the following typos?

    “We t the power-law model…”
    “Across domains, we nd that scale-free networks…”

  2. 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…

  3. 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)

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