This paper introduces a novel, Graph Theory-inspired framework for the systematic analysis of aircraft propulsion systems. The methodology encodes propulsion architectures via an architecture matrix that delineates component connectivity, while complementary operational and efficiency matrices quantify power distribution strategies and transmission losses, respectively. An algorithm using a fixed-point iteration is developed to simulate both unidirectional and bidirectional power flows, enabling the evaluation of complex operational modes, including conventional propulsion and in-flight battery charging. Multiple numerical examples demonstrate the framework’s robustness and flexibility in modeling configurations with multiple sources, sinks, and varying power path lengths. Furthermore, integration with the Future Aircraft Sizing Tool underscores its potential for use during early-phase design and trade space exploration. By overcoming previous limitations such as restrictions on serial power-transmitting components, this unified and adaptable framework advances the state of the art in propulsion system analysis and lays a solid foundation for future improvements in computational efficiency and component classification.