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.
Scale-free networks are rare
Anna D. Broido, Aaron Clauset
Twitter discussion, including Aaron Clauset, Laszlo Barabasi, Alex Vespignani, Duncan Watts, Stefano Zapperi, Petter Holme, Gabor Vattay, et al.
Blog post by Petter Holme