Hypothesis
Scale-free (power-law degree) structure is a near-universal property of real-world networks, with broad consequences for the structure and dynamics of complex systems.
What failed
Applying statistical tests across nearly 1,000 social, biological, technological, transportation and information networks, strongly scale-free structure was empirically rare: for most networks log-normal distributions fit as well or better than power laws, and social networks were at best weakly scale-free.
Broken assumption
Power-law degree distributions are a universal signature of real-world networks.
Why
The authors organise the competing definitions of 'scale-free' and show the prevalence claim does not survive severe testing; a handful of technological and biological networks do appear strongly scale-free, so they call for new theory for the non-scale-free majority.
From the published paper: Broido et al. Nature Communications, 2019. ↗CC BY