  The number of units of a network dynamical system, its size, arguably
constitutes its most fundamental property. Many units of a network, however,
are typically experimentally inaccessible such that the network size is often
unknown. Here we introduce a \emph{detection matrix }that suitably arranges
multiple transient time series from the subset of accessible units to detect
network size via matching rank constraints. The proposed method is model-free,
applicable across system types and interaction topologies and applies to
non-stationary dynamics near fixed points, as well as periodic and chaotic
collective motion. Even if only a small minority of units is perceptible and
for systems simultaneously exhibiting nonlinearities, heterogeneities and
noise, \emph{exact} size detection is feasible. We illustrate applicability for
a paradigmatic class of biochemical reaction networks.
