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.
Highlights
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
Many studies investigate how the presence of scale-free structure shapes dynamics running over a network[6,7,14,16,17,18,19,20,21,22]
A key component of our evaluation of the scale-free hypothesis is the use of a large and diverse corpus of real-world networks. This corpus is composed of 928 network data sets drawn from the Index of Complex Networks (ICON), a comprehensive online index of research-quality network data, spanning all fields of science[59]
Summary
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. 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. Few studies have performed statistically rigorous comparisons of fitted power-law distributions to alternative, non-scale-free distributions, e.g., the lognormal or stretched exponential, which can imitate a power-law form in realistic sample sizes[49] These issues raise a natural question of the pervasiveness of strong empirical evidence for scale-free structures in real-world networks. Scale invariance can refer to nondegree-based aspects of network structure, e.g., its subgraphs may be structurally self-similar[50,51], and sometimes these networks are called scale free
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
