  Recently, hetero-functional graph theory (HFGT) has developed as a means to
mathematically model the structure of large-scale complex flexible engineering
systems. It does so by fusing concepts from network science and model-based
systems engineering (MBSE). For the former, it utilizes multiple graph-based
data structures to support a matrix-based quantitative analysis. 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. These diverse conceptual constructs
indicate multi-dimensional rather than two-dimensional relationships. This
paper provides the first tensor-based treatment of hetero-functional graph
theory. 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. The
tensor-based formulation described in this work makes a stronger tie between
HFGT and its ontological foundations in MBSE. Finally, the tensor-based
formulation facilitates several analytical results that provide an
understanding of the relationships between HFGT and multi-layer networks.
