From my understanding a Sparse matrix is converted to banded matrix and then the cuthill mckee is used to reduce the bandwidth. I have spent about three days browsing the web to find an example where each step is shown with algebraic computation. Such as the permutation matrix used to convert sparse matrix to the banded matrix. And the algebraic steps for the bandwidth reduction.
I would highly appreciate if you would take some time to explain the steps (upto bandwidth reduction) to me with algebraic computations. Or if you could point me to some source.