  This work focuses on the generic identifiability of dynamical networks with
partial excitation and measurement: a set of nodes are interconnected by
transfer functions according to a known topology, some nodes are excited, some
are measured, and only a part of the transfer functions are known. Our goal is
to determine whether the unknown transfer functions can be generically
recovered based on the input-output data collected from the excited and
measured nodes. We propose a decoupled version of generic identifiability that
is necessary for generic local identifiability and might be equivalent as no
counter-example to sufficiency has been found yet in systematic trials. This
new notion can be interpreted as the generic identifiability of a larger
network, obtained by duplicating the graph, exciting one copy and measuring the
other copy. We establish a necessary condition for decoupled identifiability in
terms of vertex-disjoint paths in the larger graph, and a sufficient one.
