Scale-free networks are rare. Broido, A. D. & Clauset, A. Nature Communications, 10(1):1017, March, 2019. 929 citations (Semantic Scholar/DOI) [2025-10-11] 612 citations (Crossref/DOI) [2025-01-21] 599 citations (Crossref/DOI) [2024-10-18] 599 citations (Crossref/DOI) [2024-10-18] 753 citations (Semantic Scholar/DOI) [2024-03-18] Publisher: Nature Publishing Group![Scale-free networks are rare [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex 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.
@article{broido_scale-free_2019,
title = {Scale-free networks are rare},
volume = {10},
copyright = {2019 The Author(s)},
issn = {2041-1723},
url = {https://www.nature.com/articles/s41467-019-08746-5},
doi = {10.1038/s41467-019-08746-5},
abstract = {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.},
language = {en},
number = {1},
urldate = {2024-03-18},
journal = {Nature Communications},
author = {Broido, Anna D. and Clauset, Aaron},
month = mar,
year = {2019},
note = {929 citations (Semantic Scholar/DOI) [2025-10-11]
612 citations (Crossref/DOI) [2025-01-21]
599 citations (Crossref/DOI) [2024-10-18]
599 citations (Crossref/DOI) [2024-10-18]
753 citations (Semantic Scholar/DOI) [2024-03-18]
Publisher: Nature Publishing Group},
keywords = {Read},
pages = {1017},
}
Downloads: 0
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