Our ability to control network dynamical systems is often hindered by constraints on the number and nature of the available control actions, which make controlling the whole network unfeasible. In this manuscript, we focus on the case where unilateral inputs are exerted on a subset of the network nodes. Leveraging the observation that, different from the case of subsystems, unilateral node reachability and controllability are equivalent, we provide conditions for a given node subset to be unilaterally controllable. The theoretical findings are then employed to develop a computationally efficient heuristic to select the nodes where the unilateral inputs should be injected.