  We address the problem of retrieving the full state of a network of R\"ossler
systems from the knowledge of the actual state of a limited set of nodes. The
selection of the nodes where sensors are placed is carried out in a
hierarchical way through a procedure based on graphical and symbolic
observability approaches. By using a map directly obtained from the governing
equations, we design a nonlinear network observer which is able to unfold the
state of the non measured nodes with minimal error. For sparse networks, the
number of sensors scales with half the network size and node reconstruction
errors are lower in networks with heterogeneous degree distributions. The
method performs well even in the presence of parameter mismatch and
non-coherent dynamics and, therefore, we expect it to be useful for designing
robust network control laws.

Chaotic Dynamics