I've the following Matlab code:r = symrcm(A(2:end, 2:end)); prcm = [1 r + 1]; spy(A(prcm, prcm));where A should be sparse connectivity matrix.I understood what it does:Finds a permutation vector r of the submatrix of A A(2:end, 2:end) (produced by the reverse Cuthill-McKee algorithm)Creates a vector prcm which is basically a vector with a $1$ in the first position and all other elements of r increased by $1$. This prcm vector applied to A as A(prcm, prcm)  logically means that we're going to permutate all rows and columns of A according to the reverse Cuthill-McKee algorithm except the first row and the first column. So the resulting matrix would look something like this:Ignore the specific numbers that you see in the plot.QuestionWhy would one want such a permutation of the rows and columns of a matrix?From what I've been reading and I've observed applying, for example, the guassian elimination to this matrix would produce a disastrous fill-in after trying to remove all entries of the first row (Check chapter 5.7 from A first course in numerical methods by Ascher and Greif). So, who wrote this code definitely didn't want to find a permutation of $A$ to apply the guassian elimination...
Find a permutation matrix (using the Matlab's function $symrcm$) of a matrix $A(2:end, 2:end)$
matlab;sparse;vector;banded matrix