The topology of river networks has been a subject of intense research in hydro-geomorphology, with special attention to self-similar (SS) structures that allow one to develop concise representations and scaling frameworks for hydrological fluxes. Tokunaga self-similar (TSS) networks represent a particularly popular two-parameter class of self-similar models, commonly accepted in hydrology but rarely tested rigorously. In this paper we (a) present a statistical framework for testing the TSS assumption and estimating the Tokunaga parameters; (b) present an improved method for estimating the Horton ratios using the Tokunaga parameters; (c) evaluate the proposed testing and estimation frameworks using synthetic TSS networks with a broad range of parameters; (d) perform self-similar analysis of 408 river networks of maximum order Ω≥ 6 from 50 catchments across the US; and (e) use the Tokunaga parameters as discriminatory metrics to explore climate effects on network topology. We find that the TSS assumption cannot be rejected in the majority of the examined river networks. The theoretical expression for the Horton ratios based on the estimated Tokunaga parameters in the TSS networks provides a significantly better approximation to the true ratios than the conventional linear regression approach. A correlation analysis shows that the Tokunaga parameter c, which determines the degree of side-branching, exhibits significant dependence on the hydroclimatic variables of the basin: storm frequency, storm duration, and mean annual rainfall, offering the possibility of relating climate to landscape dissection. While other possible physical controls have been neglected in this study, this result is intriguing and warrants further analysis.