We present FLOWGEN, a graph-generation model inspired by the dual-process theory of mind that generates large graphs incrementally. Depending on the difficulty of completing the graph at the current step, graph generation is routed to either a weak or a strong model. Weak and strong models have identical architectures, but vary in the number of parameters and consequently the strength. Experiments on three diverse, real-world graphs show that FLOWGEN can successfully generate graphs similar to those generated by a single large model in a fraction of time.