The systematics of tributary junction angles are an important link between the topology of a drainage network and its topography because the angle of junction depends on the relative slopes of the intersecting tributaries. I present here a model for stream junction angle as a function of position (link magnitude) within the network which quantitatively predicts the observed down-network increase of junction angle for tributaries joining progressively larger recipient links. Good agreement between model and data exists for mature drainage networks mapped at varying scales. Additionally, the dependency of junction angle on relative tributary slopes suggests that as individual links within the network modify their slopes to evolve toward graded longitudinal profiles, there exists a central tendency within the network, modulated by structural and lithologic controls, for evolution to an equilibrium or ''graded'' planimetric pattern. Extraction of process-related (as opposed to purely toplogical) information from network planimetric pattern is important in terrestrial and planetary remote sensing applications.