As the electric grid becomes increasingly cyber-physical, it is important to characterize its inherent cyber-physical interdepedencies and explore how that characterization can be leveraged to improve grid operation. It is crucial to investigate what data features are transferred at the system boundaries, how disturbances cascade between the systems, and how planning and/or mitigation measures can leverage that information to increase grid resilience. In this paper, we explore several numerical analysis and graph decomposition techniques that may be suitable for modeling these cyber-physical system interdependencies and for understanding their significance. An augmented WSCC 9-bus cyber-physical system model is used as a small use-case to assess these techniques and their ability in characterizing different events within the cyber-physical system. These initial results are then analyzed to formulate a high-level approach for characterizing cyber-physical interdependencies.