# A Tensor-Based Formulation of Hetero-functional Graph Theory

arXiv: https://arxiv.org/abs/2101.07220 · HTML: https://mlsanity.com/paper/2101.07220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 141 references that are in the map.
- First posted on arXiv 14 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Random Walks on Multiplex Networks](https://mlsanity.com/paper/1306.0519/) (2013)
- [Spectral properties of the Laplacian of multiplex networks](https://mlsanity.com/paper/1307.2090/) (2013)
- [Eigenvector centrality of nodes in multiplex networks](https://mlsanity.com/paper/1305.7445/) (2013)
- [Structural measures for multiplex networks](https://mlsanity.com/paper/1308.3182/) (2013)
- [Growing multiplex networks](https://mlsanity.com/paper/1302.7126/) (2013)
- [ABACUS: frequent pAttern mining-BAsed Community discovery in mUltidimensional networkS](https://mlsanity.com/paper/1303.2025/) (2013)
- [Contact-based Social Contagion in Multiplex Networks](https://mlsanity.com/paper/1307.1656/) (2013)
- [Multidimensional Social Network in the Social Recommender System](https://mlsanity.com/paper/1303.0093/) (2013)
- ["You Know Because I Know": a Multidimensional Network Approach to Human Resources Problem](https://mlsanity.com/paper/1305.7146/) (2013)
- [On Synchronization of Interdependent Networks](https://mlsanity.com/paper/1304.4731/) (2013)
- [Network robustness of multiplex networks with interlayer degree correlations](https://mlsanity.com/paper/1307.1253/) (2013)
- [Layer-switching cost and optimality in information spreading on multiplex networks](https://mlsanity.com/paper/1307.2967/) (2013)
- [Communities unfolding in multislice networks](https://mlsanity.com/paper/1604.00491/) (2016)

## Abstract (arXiv)

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.