Real-world networks are scale-free: their degree distributions follow a power law p(k) ~ k
Under a rigorous Clauset-Shalizi-Newman fit (MLE alpha, KS-selected xmin, bootstrap goodness-of-fit, Vuong likelihood-ratio vs lognormal, n=20,000): a lognormal that 'looks scale-free' on a log-log plot is correctly REFUSED (power-law GOF p=0.01; LR favors lognormal, -17.5); a genuine Pareto power law passes (GOF p=0.92; LR +102); and a real Barabasi-Albert network is only a TIE (LR -0.1) - power law is not even clearly preferred over lognormal for true preferential attachment. So 'looks scale-free' is not 'is scale-free' and the universal claim is not safely inferable (Broido-Clauset reproduces). Power law IS reproduced for true BA graphs.