  In this work, we extend the so-called typicality approach, originally
formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network
states. Our results do not depend on the physical interpretation of the spin
network; however, they are mainly motivated by the fact that spin-network
states can describe states of quantum geometry, providing a gauge-invariant
basis for the kinematical Hilbert space of several background-independent
approaches to quantum gravity. The first result is, by itself, the existence of
a regime in which we show the emergence of a typical state. We interpret this
as the proof that in that regime there are certain (local) properties of
quantum geometry which are "universal". Such a set of properties is heralded by
the typical state, of which we give the explicit form. This is our second
result. In the end, we study some interesting properties of the typical state,
proving that the area law for the entropy of a surface must be satisfied at the
local level, up to logarithmic corrections which we are able to bound.
