Approximations on the Peano river network: Application of the Horton-Strahler hierarchy to the case of low connections

A network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10-3. This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale.