Several quantitative descriptors of polymer topology-the Wiener number W, complexity index K, and the index of 3-starness S-were shown to relate well the measured rheological properties of linear and 3-arm star monodisperse polyethylene samples to their structure. The complexity index K (the substructure count) provided single-variable models with correlation coefficients r ranging from 0.95 to 0.98 for zero-shear viscosity, activation energy, and the parameters A and a from the Cross equation, which describes the shape of the viscosity/shear rate curve. The regression models with two and three topological variables were characterized by r > 0.99 and low standard deviations. The models were used to predict the values of these rheological parameters for branched monodisperse polyethylenes not yet synthesized, thus indicating the potential of this topology-based methodology for industrial applications. The study also presents a statistical confirmation for the much stronger effect that long-chain branching has on shear rheology than that of molecular weight. (C) 2003 Wiley Periodicals, Inc.