Scale-free networks, where node degrees follow a power-law distribution, are rare in real-world networks. A study analyzing 927 diverse network data sets from social, biological, technological, and informational domains found that only 4% of networks exhibit strong evidence of scale-free structure, while 52% show weak evidence. Social networks are mostly not scale-free, while a few technological and biological networks are. The results challenge the universality of scale-free networks and suggest real-world networks have diverse structures that require new explanations. The study used advanced statistical methods to test the power-law fit of degree distributions against alternatives like log-normal and stretched exponential. It defined five categories of scale-free evidence, from Super-Weak to Strongest, based on statistical plausibility and model comparisons. Biological networks showed the least scale-free structure, while technological networks had more indirect evidence. Social networks were at best weakly scale-free. The findings indicate that scale-free networks are not common, and the scale-free hypothesis is not universally applicable. This challenges long-held beliefs in network science and highlights the need for new models to explain network structures. The study also shows that real-world networks exhibit a wide variety of degree distributions, many of which are not convincingly scale-free. The results suggest that the scale-free model is not a universal starting point for network analysis, and alternative mechanisms may better explain network structures. The study underscores the importance of empirical validation and the need for further research into network diversity.Scale-free networks, where node degrees follow a power-law distribution, are rare in real-world networks. A study analyzing 927 diverse network data sets from social, biological, technological, and informational domains found that only 4% of networks exhibit strong evidence of scale-free structure, while 52% show weak evidence. Social networks are mostly not scale-free, while a few technological and biological networks are. The results challenge the universality of scale-free networks and suggest real-world networks have diverse structures that require new explanations. The study used advanced statistical methods to test the power-law fit of degree distributions against alternatives like log-normal and stretched exponential. It defined five categories of scale-free evidence, from Super-Weak to Strongest, based on statistical plausibility and model comparisons. Biological networks showed the least scale-free structure, while technological networks had more indirect evidence. Social networks were at best weakly scale-free. The findings indicate that scale-free networks are not common, and the scale-free hypothesis is not universally applicable. This challenges long-held beliefs in network science and highlights the need for new models to explain network structures. The study also shows that real-world networks exhibit a wide variety of degree distributions, many of which are not convincingly scale-free. The results suggest that the scale-free model is not a universal starting point for network analysis, and alternative mechanisms may better explain network structures. The study underscores the importance of empirical validation and the need for further research into network diversity.