For linear reaction networks, graph-theoretical methods are used to find two types of kinetic transfer functions in the Laplace domain for isothermal uniform open systems under transient regime. Rules are formulated to find the functional form of these transfer functions from properties of the reaction network, viz the number of components and the length of shortest paths. In many cases, some reaction intermediates are not observed. This is typical in heterogeneous catalysis, where the intermediates are bound to the catalytic surface. The mechanistic details are then manifested only through some transfer functions. This often causes the rate coefficients to be unidentifiable. A graph-theoretical rule is derived which allows assessing whether reaction networks are structurally locally identifiable. It is applied to the interaction of propane with a copper oxide/ceria-catalyst, as studied with a temporal analysis of products (TAP) setup. (C) 2009 Elsevier Ltd. All rights reserved.