LAUSR

Significance The generalized scale invariance of complex networks, whose trademark feature is the power law distributions of key structural properties like node degree, has recently been questioned on the basis of statistical testing of samples from model and real data. This has important implications on the dynamic origins of network self-organization and consequently, on the general interpretation of their function and resilience. However, a well-known mechanism of departure from scale invariance is the presence of finite size effects. Developed for critical phenomena, finite size scaling analysis assesses whether an underlying scale invariance is clouded by a sample limited in size. Our approach sorts out when we may reject the hypothesis that the inherent structure of networks is scale invariant. We analyze about 200 naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees. Specifically, we analyze by finite size scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follows a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially involving infrastructure and transportation but also in social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite size effects due to the nature of the sample data.