ABSTRACT
In an attempt to generate a more sensitive ordering scheme and a model devoid of R. E. Horton’s inconsistencies, R. L. Shreve has proposed a random topology model based solely upon combinatorial properties. Shreve’s random topology model is based upon a little-known combinatorial expression first derived by A. Cayley in the mid-nineteenth century. The extreme tips of the network are termed sources with the exception of the outlet, the farthest point downstream. A natural extension to the random topology model is from topologically finite to topologically infinite networks. An attempt at specifying small-scale topologic features of drainage networks has been described by Krumbein and James. In addition to deriving a random link length model Smart has also attempted to model drainage basin areas using the random topology model. The mathematics has proved both elegant and exciting, but from the geomorphic viewpoint, exploration of the purely topologic properties of stream networks has proved unrewarding.
