When solving a vibroacoustic problem in a physical system, a fundamental goal is to determine how energy is transmitted from a given source to any part of the system. This enables the modifications needed to reduce noise or vibration levels in each system component. Numerical techniques such as Finite Element Method (FEM) and Statistical Energy Analysis (SEA) can predict the vibroacoustic behavior of the system; yet, they do not directly reveal which part of the system shall be modified. The energy transmitted via the path that connects a source and a target subsystem component can be determined numerically. Finding the dominant paths that contribute the most to the total energy transmitted between a source and target is more art than science; finding the dominant paths usually depends on an engineer's expertise and judgement. Thus, a systematic approach to automatically identify those paths would be beneficial. Graph theory provides a solution to this problem, because powerful path algorithms for graphs have already been developed. In this study, a systematic procedure for ranking the dominant energy paths in a vibroacoustic model is developed by using existing graph theory and SEA graph approaches. To extend the use and performance of this application-specific approach which investigates the vibroacoustic behavior of a ship structure, a research ship has been modelled via a SEA model for mid- and high-frequency ranges. Then, the structure-borne energy transmission paths from a vibration source to the keel bottom (underwater hull) plates are determined and ranked by their energy output. Next, the process identifies the structural elements that need to be modified to reduce the overall energy levels. A parametric approach is then used to modify these ideal candidates using a representative FEM model. Finally, the modelling results verify that the path-modified ship structure has reduced the structural vibration energy levels. Thus, by using and extending the pre-existing graph theory algorithm, the vibroacoustic behavior of complex ship structures is predicted, the energy output of each path is found and the problematic paths are modified during the ship design phase to ensure that vibration and noise levels are minimized.