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A model of a system of wireless power transfer (WPT) pads is developed, where each WPT pad is modeled as a node and the coupling between pads is modeled as graph edges. This modeling approach is generalized to admit primary, secondary, and booster coils, where power can flow among the pads and a pad can fill multiple roles. An excitation in one pad induces voltage and current in all neighboring pads, causing each pad to act as both a booster coil and either a transmitter or a receiver. Power flow through the entire system can be modeled with the graph structure; the power flow can then be optimized by alternating the phases of the WPT excitations to maximize power transfer. An example is shown where exploiting the graph-based WPT system modeling increases total energy transfer by 25% compared to another method. This increase occurs without altering the geometry of the pads or the magnitude of the pad excitations. [ABSTRACT FROM AUTHOR]