Connecting network graph structure to linear-system zero structure

We examine linear network dynamics in which an input can be applied at only one network component and measurements can only be made at one (in general different) component. The infinite-zero- and finite-invariant-zero-structure of these dynamics are characterized explicitly in terms of the network's graph matrix, using the special coordinate basis for linear system. These algebraic characterizations are then used to identify relationships between features of the network's graph topology and the state matrix of its finite zero dynamics.