  A faithful description of the state of a complex dynamical network would
require, in principle, the measurement of all its $d$ variables, an infeasible
task for systems with practical limited access and composed of many nodes with
high dimensional dynamics. However, even if the network dynamics is observable
from a reduced set of measured variables, how to reliably identifying such a
minimum set of variables providing full observability remains an unsolved
problem. From the Jacobian matrix of the governing equations of nonlinear
systems, we construct a {\it pruned fluence graph} in which the nodes are the
state variables and the links represent {\it only the linear} dynamical
interdependences encoded in the Jacobian matrix after ignoring nonlinear
relationships. From this graph, we identify the largest connected sub-graphs
where there is a path from every node to every other node and there are not
outcoming links. In each one of those sub-graphs, at least one node must be
measured to correctly monitor the state of the system in a $d$-dimensional
reconstructed space. Our procedure is here validated by investigating
large-dimensional reaction networks for which the determinant of the
observability matrix can be rigorously computed.
