Scale-free networks are rare

2018/01/09 by Anna D. Broido, Aaron Clauset · 2 voices · 36 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cs.SI #physics.data-an #physics.soc-ph #q-bio.MN #stat.AP

paper · pdf · doi:10.1038/s41467-019-08746-5

published as Nature Communications 10, 1017 (2019) · 14 pages, 9 figures, 2 tables, 5 appendices

arxiv created 2018/01/09 · openalex created_date 2018/01/26 · openalex publication_date 2019/03/04 · arxiv updated 2019/03/19 · openalex updated_date 2026/07/28

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, decaying like k^-α, 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.

Citations

• Power-Law Distributions in Empirical Data
• Error and attack tolerance of complex networks
• Evolution of networks
• Power laws, Pareto distributions and Zipf's law

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Discussions

• Scale-Free Networks Are Rare [hn, 4 points, 2 comments]
• Excited to share this new work: "Scale-free networks are rare," from Anna Broido and me. We applied rigorous statistical tools to test for scale-free patterns in nearly 1000 network datasets: https:// [bsky, 0 points, 0 comments]

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