A new approach to derive the equations of multicoil wireless power transfer (MCWPT) systems and to simplify and analyze them is proposed in this article. By parametrically solving the equations governing MCWPT systems and mapping the resultant transfer functions into graph sets (GSs), a set of rules is developed to form the transfer function among the voltages across and currents through the coils. Using these rules, some important aspects, such as effective paths for the power to flow, the effect of active coils on each other and on passive coils, dynamic behavior of the system, and reflected impedances, can be comprehensively analyzed. This can be done by following GS rules and without complex mathematical calculations. The GS method (GSM) also provides an effective tool to design compensators and power electronic converters driving MCWPT systems and to estimate the receiver (pickup) parameters. Moreover, simplifying the behavior of the coils into three basic types, current-driven, voltage-driven, and passive coils, helps to reduce the complexity of the model and to have a better understanding of the system. This simplification can be further expanded by removing ineffective couplings between the coils. This article is presented in two parts. In Part I, the GSM is explained, and its different analytical steps are established, and Part II is dedicated to show the effectiveness and validity of this approach by numerically modeling and experimentally evaluating a three-coil MCWPT system.