  This paper deals with dynamical networks for which the relations between node
signals are described by proper transfer functions and external signals can
influence each of the node signals. In particular, we are interested in
graph-theoretic conditions for identifiability of such dynamical networks,
where we assume that only a subset of nodes is measured but the underlying
graph structure of the network is known. This problem has recently been
investigated in the case of generic identifiability. In this paper, we
investigate a stronger notion of identifiability for all network matrices
associated with a given graph. For this, we introduce a new graph-theoretic
concept called constrained vertex-disjoint paths. As our main result, we state
conditions for identifiability based on these constrained vertex-disjoint
paths.
