  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 by contrasting real data. Specifically, we
analyze by finite-size scaling analysis the datasets of real networks to check
whether purported departures from the power law behavior are due to the
finiteness of the sample size. In this case, power laws would be recovered in
the case of progressively larger cutoffs induced by the size of the sample. We
find that a large number of the networks studied 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 infrastructure and transportation but also 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.
