  We develop a local probe to estimate the connectivity of complex quantum
networks. Our results show how global properties of different classes of
complex networks can be estimated - in quantitative manner with high accuracy -
by coupling a probe to a single node of the network. Here, our interest is
focused on probing the connectivity, i.e. the degree sequence, and the value of
the coupling constant within the complex network. The scheme combines results
on classical graph theory with the ability to develop quantum probes for
networks of quantum harmonic oscillators. Whilst our results are
proof-of-principle type, within the emerging field of quantum complex networks
they may have potential applications for example to the efficient transfer of
quantum information or energy or possibly to shed light on the connection
between network structure and dynamics.
