Scale-free networks are rare

By Anna D. Broido, Aaron Clauset. Nature Communications, 2018

1,034 citations recorded by the source corpus.

Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k−α, a pattern with broad implications for the structure and dynamics of complex systems. However, the universality of scale-free networks remains controversial. 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. Furthermore, social networks are at best weakly scale free, while a handful of technological and biological networks appear strongly scale free. These findings highlight the structural diversity of real-world networks and the need for new theoretical explanations of these non-scale-free patterns. Real-world networks are often said to be ”scale free”, meaning their degree distribution follows a power law. Broido and Clauset perform statistical tests of this claim using a large and diverse corpus of real-world networks, showing that scale-free structure is far from universal.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1b4361a1978e93018c5fdfe4856250152676ffb

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In Statistical and Nonlinear Physics

  1. Daniel Zügner
  2. Stephan Günnemann
  3. Oleksandr Shchur
  4. Aleksandar Bojchevski
  5. Johannes Klicpera
  6. Matthias Fey
  7. Jure Leskovec
  8. Muhan Zhang

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