I am working with hypergraphs. The various matrices associated with hypergraphs are hypermatrix or tensors. I am interested in spectral aspects. In particular, I want to find all the eigenvalues explicitly for a class of hypergraphs. To start with, we can consider all the $0-1$ hypermatrices of order $2 \times 2 \times 2$. Then the characteristic polynomial is defined in terms of [resultants](https://arxiv.org/pdf/1301.4590.pdf) of a certain system of homogeneous equations.


I want to know, some simple or at least a concrete way of calculating these eigenvalues. I have understood the method given in this [paper](https://arxiv.org/pdf/1301.4590.pdf). But this method was applicable only to special hypermatrices. Kindly share some references. Thank you.


Edit: I am interested in general uniform hypergraph then its associated matrices can be of any order and dimension. I thought, to start with, I will look at the simplest $2 \times 2 \times 2$ case. 



Simple way to calculate the eigenvalues of a $2 \times 2 \times 2$ tensor
As explained in a [previous MO question](https://mathoverflow.net/questions/319644/eigenvalue-and-eigenmatrix-of-a-3d-tensor-how-to-calculate-it), there is no unique generalization of the eigenvalue of an $n\times n$ matrix to an $n\times n\times n$ tensor. One approach is to construct a [higher-order singular value decomposition.](https://en.wikipedia.org/wiki/Higher-order_singular_value_decomposition) This has been worked out for the specific case of $2\times 2\times 2$ tensors by Ana Rovi in a [M.Sc. thesis.](https://pdfs.semanticscholar.org/f812/053bd5ae1d9eb85b85d69726c6c8bd5aa88c.pdf) Even for this simple case, there is no simple closed-form expression. A [MatLab toolbox](https://www.tensortoolbox.org/hosvd_doc.html) may be useful to implement the procedure.


