Counting adjacent elements in a Matrix?

To start, I have a situation where I have some matrix, for example

$$ A=\left[ \begin{matrix} 4&2&2&3&3\\ 2&3&1&2&3\\ 3&0&4&0&4\\ 1&4&1&1&2\\ 1&3&4&1&4\\ \end{matrix} \right] $$

and I would like to count how many adjacent elements there are. Adjacent elements can be up, down, left or right. For a pair to be valid the numbers have to have the same value. For example $\left(A_{1,2},A_{1,3}\right)$ is a valid pair because the are both $2$ and they are next to each other. I need a way to count the defined adjacent element pairs on a matrix of size $n$.

eg.

$$ \left[ \begin{matrix} 2&2&3\\ 3&2&3\\ 2&1&1 \end{matrix} \right] $$

There would be 4 pairs in this matrix.

I thought about converting the matrix into some sort of graph with "weighted vertices" however I had no clue on doing so. It would have then made it a matter of counting arcs. So how would one produce a function that takes in a matrix and spits out the number of pairs (by my definition) it contains?

I am unsure whether or not I have tagged this correctly.