We numerically study how the cutoff scaling of the upper degree affects the finite-size scaling (FSS) for physical models of scale-free networks (SFNs) in terms of the Ising model for annealed and quenched SFNs. Based on the hyperscaling argument and the results of S. H. Lee et al. [Phys. Rev. E 80, 051127 (2009) ], we test the suggested FSS theory according to the value of the cutoff exponent, and find the cutoff of upper degree scales as a power law in the system size. In particular, we focus

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... on finding the relevant length scale in finite SFNs near and at criticality. Moreover, we investigate the self-averaging property of the system in the presence of a quenched linking disorder as a way for exploring the fluctuations in the sampling disorder for the finite-degree sequence set.