![]() One defining characteristic of twenty-first century engineering challenges is the breadth of their scope. Finally, the tensor-based formulation facilitates several analytical results that provide an understanding of the relationships between HFGT and multi-layer networks. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. In particular, it addresses the “system concept” and the hetero-functional adjacency matrix from the perspective of tensors and introduces the hetero-functional incidence tensor as a new data structure. This paper provides the first tensor-based treatment of hetero-functional graph theory. These diverse conceptual constructs indicate multi-dimensional rather than two-dimensional relationships. For the latter, HFGT inherits the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. For the former, it utilizes multiple graph-based data structures to support a matrix-based quantitative analysis. It does so by fusing concepts from network science and model-based systems engineering (MBSE). Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. ![]()
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