Informational entropy of fractal river networks

Informational entropy of river networks, as defined by Fiorentino and Claps (1992), proved to be a useful tool in the interpretation of several properties exhibited by natural networks. In this paper, self-similar properties of river networks are taken as the starting point for investigating analogies and differences between natural networks and geometric fractal trees, comparing their variability entropy with parameters of both classes of networks. Attention is directed particularly to relations between entropy and Horton order and entropy and topological diameter of subnetworks. Comparisons of these relations for fractals 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 branching for natural networks can be considerably improved using the relation between entropy and Horton order throughout the network.