As modern operational systems become more interconnected, a system of systems (SoS) approach must be adopted. As part of this, a methodology is needed to decompose, partition, and analyze operational SoS problem spaces. This paper presents a graph-based digital engineering ontology developed to address this need. This is done by developing several logical Systems Modeling Language (SysML) model components and integrating them into a graph-based analysis framework using the developed ontology. This analysis framework serves as a structured way to break down and analyze the combinatorial problem space of the SoS. Given this SysML and graph-based framing of the kill web problem, research opportunities are discussed regarding future work that is needed to use the ontology to actually execute missions.