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 high dimensional systems due to practical limitations. However the network dynamics might be observable from a reduced set of measured variables but how to reliably identify the minimum set of variables providing full observability still remains an unsolved problem. In order to tackle this issue from the Jacobian matrix of the governing equations, we construct a pruned fluence graph in which the nodes are the state variables and the links represent only the linear dynamical interdependences after having ignored the nonlinear ones. From this graph, we identify the largest connected subgraphs with no outgoing links in which every node can be reached from any other node in the subgraph. In each one of them, 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 tested by investigating large-dimensional reaction networks. Our results are validated by comparing them with the determinant of the observability matrix which provides a rigorous assessment of the system's observability.

• Received 5 March 2018

DOI:https://doi.org/10.1103/PhysRevE.98.020303