Before revision: We consider networks with a specific type of nodes that can have either a discrete or continuous set of states. It is shown that no matter how complex the network is, its dynamical response to arbitrary inputs is defined in a simple way by its response to a monotone input.
After revision: We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input.