And it's not just graphs...as referenced in the linked comments above, there are now linear algebra models that encode Datalog and/or the entire typed-lambda calculus as linear algebra matrix operations (and as shown in the Datalog paper [1], the Datalog linear algebra implementation is the fastest Datalog implementation to date).

But MIT and Sandia Labs are taking the linear algebra model to the next level, and are now working on encoding an entire operating system in the language of linear algebra...

Jeremy Kepner (the head of MIT Lincoln Labs and GraphBLAS lead) and his team just published a paper [2] where they define an entire unix operating system using the same linear algebra model as they used for D4M/GraphBLAS. The linear-algebra OS model scales linearly way beyond the Linux limits, and since the entire OS kernel representation is defined as generic matrix transformations, it can run on any processor, including CPUs, GPUs, or a cluster of TPUs.

[1] A Linear Algebraic Approach to Datalog Evaluation (2017) [pdf] https://arxiv.org/abs/1608.00139

[2] TabulaROSA: Tabular Operating System Architecture for Massively Parallel Heterogeneous Compute Engines (2018) [pdf] https://arxiv.org/pdf/1807.05308.pdf

Nice! I think the resource management and accounting parts in OS might be a good fit. Access control definitely is a matrix.