Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k−$\alpha$, 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.
%0 Journal Article
%1 broido2019scalefree
%A Broido, Anna D.
%A Clauset, Aaron
%D 2019
%J Nature Communications
%K analysis free graph network powerlaw scale sna social
%N 1
%P 1017
%R 10.1038/s41467-019-08746-5
%T Scale-free networks are rare
%U https://doi.org/10.1038/s41467-019-08746-5
%V 10
%X Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k−$\alpha$, 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{broido2019scalefree,
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−$\alpha$, 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.},
added-at = {2021-08-11T13:40:46.000+0200},
author = {Broido, Anna D. and Clauset, Aaron},
biburl = {https://www.bibsonomy.org/bibtex/2a96d2914089c858c09aad6baec63ed72/jaeschke},
day = 04,
doi = {10.1038/s41467-019-08746-5},
interhash = {c7c2c4a8e3c3d1098410830db4db75f7},
intrahash = {a96d2914089c858c09aad6baec63ed72},
issn = {2041-1723},
journal = {Nature Communications},
keywords = {analysis free graph network powerlaw scale sna social},
month = mar,
number = 1,
pages = 1017,
timestamp = {2021-08-11T13:40:46.000+0200},
title = {Scale-free networks are rare},
url = {https://doi.org/10.1038/s41467-019-08746-5},
volume = 10,
year = 2019
}