  Recently, hetero-functional graph theory (HFGT) has developed as a means to
mathematically model the structure of large flexible engineering systems. In
that regard, it intellectually resembles a fusion of network science and
model-based systems engineering. With respect to the former, it relies on
multiple graphs as data structures so as to support matrix-based quantitative
analysis. In the meantime, HFGT explicitly embodies the heterogeneity of
conceptual and ontological constructs found in model-based systems engineering
including system form, system function, and system concept. At their
foundation, these disparate conceptual constructs suggest multi-dimensional
rather than two-dimensional relationships. This paper provides the first
tensor-based treatment of some of the most important parts of hetero-functional
graph theory. In particular, it addresses the "system concept", the
hetero-functional adjacency matrix, and the hetero-functional incidence tensor.
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 an understanding of the relationships between HFGT and
multi-layer networks.
