Systems chemistry seeks to find fundamental insights into the emergent properties of complex systems and living matter. Thus chemists use a "bottom-up" approach for the design and integration of simple elements as a means of producing self-organized systems that can serve as feasible models. Toward this end, networks of replicating molecules have been produced and their dynamic behavior was analyzed both experimentally and by simulation. In this paper we describe our analysis of the reaction mechanisms which build up these systems. To do so, we revisit models for self-replication and template assisted catalysis and expand them to describe the kinetics of small catalytic networks. From symmetry requirements and reasonable chemical assumptions, it is shown that the construction of increasingly complex networks requires higher order catalysis. Specifically, we explain why low order catalysis, in which a monomeric molecule serves as a template, is incapable of efficiently activating cooperative cross catalytic elements and basic asymmetric sequentially linked units, so that at least second order catalysis, in which dimeric molecules serve as templates, is necessary. These cooperative and asymmetric linked units are required components of more complex molecular networks. We compare our results with other experimental evidence for the centrality of higher order catalysis and discuss the implications of our results on molecular self-organization and other aspects of systems chemistry.