A mathematical model for channel networks represented by directed graphs on a rectangular grid is used to generate synthetic hydrographs. This makes possible simulation of the effects of changes in geometric factors specified by shape and connectivity, while keeping fixed a prescribed temporal and spatial precipitation pattern. Alternatively, this model may be used with fixed networks of interest to study effects of different types and motions of storms. The model provides for a discrete approximation of a distributed network, a transformation relating the runoff hydrograph and input precipitation. No combinations of generating parameters had to be determined, since only a single parameter associated with the collection and release of water to the channel was used. Although this parameter, which was the collection area storage constant, and the speed of travel for precipitation could be given different values at each point on the network, and might be varied as a function of time, both were assumed to be fixed in time and spatially uniform. The formation of hydrographs is determined by interlocking relationships between the network's geometry, its storage functions, and temporal and spatial variations of precipitation reaching and traversing a graphically specified network.