scale-free networks are rare
I linked to this article for our recent discussion of brain networks. The abstract is below.
“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.”
Santa Fe Institute (SFI) has a recent, several part online course on fractals and scaling, summarized in this video. Some real world objects indeed display fractal-like scaling but are limited within real world constraints, unlike abstract, mathematical fractals ad infinitum (2:00). Other real world applications do not exhibit fractal scaling, so other models are better suited to measure them (10:00). Here Clauset et al’s earlier work was cited, Clauset’s later empirical work (cited previously) on about 1000 networks confirming that scale-free networks are indeed rare so thus different models are needed to evaluate them. Hence questions arise if one wants… Read more »
Good luck with getting the power law religion, like any religion, to change. It too, like most religion, has to have a universal to rule them all. Proponents even admit it is idealized, that the real world doesn’t fit it. It’s just barely warmed over, metaphysically dichotomous Gnosticism hiding under the rubric of science and math. From this piece: “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.” “Supporters of the scale-free viewpoint, many of whom came to network science by… Read more »