Informational entropy of river networks, as defined by Fiorentino and
Claps (1992a), proved to be a useful tool in the interpretation of sev
eral properties exhibited by natural networks. In this paper, self-sim
ilar properties of river networks are taken as the starting point for
investigating analogies and differences between natural networks and g
eometric fractal trees, comparing their variability entropy with param
eters of both classes of networks. Attention is directed particularly
to relations between entropy and Horton order and entropy and topologi
cal diameter of subnetworks. Comparisons of these relations for fracta
ls and natural networks suggest that network entropy can contribute to
clarify important points concerning self-similar properties of river
networks. Moreover, the estimation of the fractal dimension of branchi
ng for natural networks can be considerably improved using the relatio
n between entropy and Horton order throughout the network.