The paper describes a technique whereby directed graphs can be used to represent the interactions within an active microwave device, described by means of a lumped equivalent circuit. Analytical transfer functions representing the two-port scattering parameter matrix are evaluated. These are then used in a robust, automatic small-signal parameter estimation scheme. The resulting device equivalent circuits are of minimal complexity and provide excellent fits to measured S-parameter data over a broad frequency range. Results are presented for two commercially available MESFET devices, the Plessey P35-1140 chip and the NE71000 chip.