All ships rely on many on board systems to reliably complete their missions (e.g. transporting containers, laying pipes or protecting the seas). However, for many of these ships, the detailed design of these systems is put off until the later stages of the design. For most ships, this will create no problems. However, for those complex vessels for which the system design dictates and drives the size and performance of the vessel, changes in a later design stage can be difficult and costly. For these complex ships (e.g. naval ships, pipe-laying vessels, etc), more focus should be spent on system design earlier in the ship design process. A important aspect of the system design is determining and designing the system topology (e.g. how components within a distributed system are connected). To achieve this, the ongoing PhD research of de Vos [2017] created the "Ship Distributed Systems Automatic Topology Generator" (SDS-ATG) tool. This tool combines the fundamentals of network theory and marine engineering to automatically generate a multitude of ship distributed system topology concepts. A genetic algorithm is then used to optimize these topologies with respect to system performance and cost. The performance objective can be related to the vulnerability (or robustness) of the found system topologies. This MSc thesis focusses on the investigation and development of a vulnerability assessment method, based on network theory, that can be used to assess the generated ship distributed system topologies. The assessment method will be used to better define the performance of a system design, based on the vulnerability of system topologies in early stage design. To create the method proposed within this thesis, it is necessary to evaluate the created SDS-ATG tool, as well as vulnerability prediction methods and metrics available from literature (and used in other fields). Next, the newly developed vulnerability assessment method is discussed. This discussion is based on the assumptions made to define the method, the steps taken within the method, and the advantages and disadvantages of the method. Finally, the new vulnerability assessment method is verified using hand calculations, and the results of a practical system design test-case are used to show the improvements that can be made with regards to the vulnerability of the system topology design. To conclude, the developed vulnerability assessment method is seen to greatly increase the capability of the SDS-ATG tool as an eraly stage design tool.