  The classical notions of structural controllability and structural
observability are receiving increasing attention in Network Science, since they
provide a mathematical basis to answer how the network structure of a dynamic
system affects its controllability and observability properties. However, these
two notions are formulated assuming systems with linear dynamics, which
significantly limit their applicability. To overcome this limitation, here we
introduce and fully characterize the notions "structural accessibility" and
"structural observability" for systems with nonlinear dynamics. We show how
nonlinearities make easier the problem of controlling and observing networked
systems, reducing the number of variables that are necessary to directly
control and directly measure. Our results contribute to understanding better
the role that the network structure and nonlinearities play in our ability to
control and observe complex dynamic systems.
