Is there a procedure to find the eigenvalues of A?

$$A=\begin{bmatrix}X & I &&&&&&&&& 0\\I & 0 & P &&&&&&&&\\& P^t & 0 & I &&&&&&&\\&&I & 0 & P &&&&&&&\\&&& P^t & 0 & \ddots &&&&&\\&&&& \ddots & \ddots & \ddots &&&&\\&&&&& \ddots & 0 & I &&&\\&&&&&& I & 0 & P &&\\&&&&&&& P^t & 0 & I &0_{k\times y-k}\\&&&&&&&& I &&\\0&&&&&&&& 0_{y-k\times k} && Y_{y\times y}\end{bmatrix}$$ (All rows and columns except the last are $k \times k$ blocks.)

where $A$ is adjacency matrix of cubic graphs and $X, P$ are circulant matrices of order k, Y is a matrix of order y, $k \not=y$ and $I$ is a identity matrix and $0$ is a zero matrix.

For example: How to find eigenvalues of following block matrices? enter image description here

`eig()`

? $\endgroup$ – percusse Jun 25 '18 at 16:15