The C-13-labeling technique was introduced in the field of metabolic engineering as a tool for determining fluxes that could not be found using the 'classical' method of flux balancing. An a priori flux identifiability analysis is required in order to determine whether a C-13-labeling experiment allows the identification of all the fluxes. In this article, we propose a method for identifiability analysis that is based on the recently introduced 'cumomer' concept. The method improves upon previous identifiability methods in that it provides a way of systematically reducing the metabolic network on the basis of structural elements that constitute a network and to use the implicit function theorem to analytically determine whether the fluxes in the reduced network are theoretically identifiable for various types of real measurement data. Application of the method to a realistic flux identification problem shows both the potential of the method in yielding new, interesting conclusions regarding the identifiability and its practical limitations that are caused by the fact that symbolic calculations grow fast with the dimension of the studied system.