The knowledge of structural controls of river networks (RNs) on transport dynamics is important for modeling and predicting environmental fluxes. To investigate impacts of RN’s topology on transport processes, we introduce a systematic framework based on the concept of dynamic clusters, where the connectivity of subcatchments is assessed according to two complementary criteria: minimum- and maximum-flow connectivity. Our analysis from simple synthetic RNs and several natural river basins across the United States reveals the key topological features underlying the efficiency of flux transport and aggregation. Namely, the timing of basin-scale connectivity at low-flow conditions is controlled by the abundance of topologically asymmetric junctions (side-branching), which at the same time, result in a slow-down of the flux convergence at the outlet (maximum-flow). Our results, when compared with observed topological trends in RNs as a function of climate, indicate that humid basins exhibit topologies which are “naturally engineered” to slow-down fluxes.