“Scale-Free Networks Are Rare”, 2019-03-04 (; backlinks; similar):
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 1,000 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.
[Keywords: complex networks, network topology, power law, statistical methods]
…The log-normal is a broad distribution that can exhibit heavy tails, but which is nevertheless not scale free. Empirically, the log-normal is favored more than 3× as often (48%) over the power law, as vice versa (12%), and the comparison is inconclusive in a large number of cases (40%). In other words, the log-normal is at least as good a fit as the power law for the vast majority of degree distributions (88%), suggesting that many previously identified scale-free networks may in fact be log-normal networks.