Having established the foundation for the three network measures, we then applied the measures to characterize the species-species network (Supplementary Information, S3.1). Crucially, the oscillator can only exist when the network is maintained under out-of-equilibrium conditions. Therefore, we introduced two nodes (source, S, and waste, W) to take the inflow of the reactants and the outflow of the products of the network into account. Fig. shows that the graph for the CRN out-of-equilibrium (G2) comprises more nodes (12 instead of 10) and more weighted edges (32 instead of 19) than the graph for the CRN in equilibrium (G1). Details of the graphs are appended to Supplementary Information, Table and S2.