# True scale-free networks hidden by finite size effects

Naturally occurring networks have an underlying scale-free structure that is often clouded by finite-size effects in the sample data.

*Proceedings of the National Academy of Sciences of the USA* 118, 2 (2021)

M.Serafinoa, G. Cimini, A. Maritan, A. Rinaldo, S.Suweis, J. R. Banavar, G. Caldarelli

We analyze about two hundred 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 follow 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 the 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.