AbstractImproved techniques to develop future System of Systems solution architectures are a systems engineering imperative. The systems engineer must be able to produce quantitative Measures of Performance that parse good performing architectures from bad architectures in a very complex and dynamic domain often and early during concept development. This paper proposes innovative System of Systems Engineering techniques to manage risks and reduce costs in complex systems. We suggest a combination of graph theory, Big Data and Uncertainty Quantification are foundational tools that can model architectures and more importantly the movement of data across architecture interfaces. This provides a mathematical foundation for quantitative architecture, model based systems engineering and simulation environments enabling continuous prototype testing in a model environment. The result is a means to quantitatively validate viable complex architectures early in the lifecycle. This paper describes a graph-based approach to model complex architectures. Complexity will be defined mathematically as a function of the number of entities, inter-entity relationships and active event sequences in the graphical architecture. Uncertainty quantification compares the graph model to the physical System of Systems based on quantities of interest. Big Data facilitates analytics across continuous data threads in the architecture.