  Given an additive network of input-output systems where each node of the
network is modeled by a locally convergent Chen-Fliess series, two basic
properties of the network are established. First, it is shown that every
input-output map between a given pair of nodes has a locally convergent
Chen-Fliess series representation. Second, sufficient conditions are given
under which the input-output map between a pair of nodes has a well defined
relative degree as defined by its generating series. This analysis leads to the
conclusion that this relative degree property is generic in a certain sense.
