  Quantum networks illustrate the use of connected nodes of quantum systems as
the backbone of distributed quantum information processing. When the network
nodes are entangled in graph states, such a quantum platform is indispensable
to almost all the existing distributed quantum tasks. Unfortunately, real
networks unavoidably suffer from noise and technical restrictions, making nodes
transit from quantum to classical at worst. Here, we introduce a figure of
merit in terms of the number of classical nodes for quantum networks in
arbitrary graph states. Such a network property is revealed by exploiting a
novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate
photonic quantum networks of $n_q$ quantum nodes and $n_c$ classical nodes with
$n_q$ up to 6 and $n_c$ up to 18 using spontaneous parametric down-conversion
entanglement sources. We show that the proposed method is faithful in
quantifying the classical defects in prepared multiphoton quantum networks. Our
results provide novel identification of generic quantum networks and
nonclassical correlations in graph states.
