Abstract: Some new methods for the topologic classification of channel networks are proposed. These methods are all based on the concept of topologic path length, or number of links from the network outlet to a junction or source. Two parameters, the total path length (sum of all path lengths) and the diameter (largest path length) are shown to be useful in network analysis. Some advantages of these parameters are that they are easy to measure, have straightforward topologic interpretations, and are closely related to important geometric measures. Moreover, they are capable of explaining various empirical geomorphic “laws,” such as the 0.6 power relation between mainstream length and area.

Abstract: The random model of drainage basin composition is founded on the assumptions that (a) natural channels are topologically random in the absence of geological controls and (b) for channel networks developed in similar environments, the exterior and interior link lengths are independent random variables with a common distribution for each type. The effectiveness of this model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships is illustrated by several examples. The data required for these examples were obtained from map studies of 30 channel networks, comprising a total of about 8700 links, in eastern Kentucky. A common factor in the success of all three applications of the model is the way in which the planimetric features of drainage basins are determined by their underlying topologic structure.