The influence of the Wiener index on solution properties of trifunctional hyperbranched polymers has been investigated using Brownian dynamics simulations with excluded volume and hydrodynamic interactions. A range of degrees of polymerization (N) and degrees of branching (DB) were used. For each DB and N, several molecules with different Wiener indices (W) were simulated, where W depends on the arrangement of branch points. The intrinsic viscosity and the radius of gyration (R-g) of HPs were both observed to scale with W at a constant N via a power law relationship, as found in the literature. Through their relationships to W, an expression relating intrinsic viscosity to R-g was obtained. This relationship is found to fall centrally between the predictions of Flory and Fox for linear polymers and that of Zimm and Kilb for branched polymers. Molecular shape in solution is also found to depend on W and N, as observed through the W dependence of the ratio of R-g to the hydrodynamic radius, R-h.