The characteristics of van Gurp-Palmen (vGP) plot for long-chain branching polymer with well-defined topological structures, including symmetric star, asymmetric star, H-shaped, and comb polymers, have been calculated by "branch-on-branch" constitutive model. It is indicated that there is only one characteristic transition in the vGP plot for nearly symmetric star polymers, but more for other chain topologies, which were deeply dependent on the topology and the molecular parameters such as side-arm length, backbone length, and number of side arms. The theoretically calculated characteristic transition points were used to construct a topology map. A feasible protocol to distinguish the topological structures of branched polymer was put forward to quantify the chain structure qualitatively and quantitatively. Such a method has been successfully proved by its application on the available data in the literature. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3569136]