Atom transition networks (ATNs) provide the fine-grained, atom-level description of a chemical reaction network that is required for a detailed, mechanistic understanding of multi-step reactions and for the practical analysis of isotope labeling experiments. Conceptually, ATNs are determined completely by (i) the reaction-level description of a chemical reaction networks, (ii) the atom-to-atom map for each constituent reaction, and (iii) fluxes specifying the relative contribution of different reactions to the turnover of individual reactants. The construction of ATNs, and thus the analysis of isotope tracing experiments, is a notoriously difficult and time-consuming task that is aggravated by symmetries in molecules and reactions. Starting from the atom-to-atom map of a reaction we first derive a transition matrix that exactly describes the propagation of the label from reactants to products, taking into account the relevant symmetries. These are subsequently combined into a ATN. Assuming a steady-state flux $\FLW$ through the chemical reaction network we derive a system of affine differential equations describing how the reaction network is flooded by labeled atoms from an external reservoir. This leads to a unique asymptotically stable steady-state distribution of labels that can be computed by solving a non-singular system of linear equations. Linear combinations of these single-atom labeling patterns also solve the problem of computing the enrichment of multiple, simultaneous labels, albeit without providing information on correlations between distinct labels. In particular, we present a simple and complete solution for an important special case of isotope tracing experiments, namely the specific labeling of a single atom in a single feed compound.