Flexibility of use is essential for the usefulness of a numerical method for applied projects. Thus we favorize a modularizable algorithmic approach to algebraic multigrid methods. It is based on the matrix graph and at various stages of the solution process different parts of the multigrid preconditioner are established.
Based on numerical experiments, we compare the two main approaches to this aim, namely the vertex centered approach with matrix dependent transfer operators and the cell centered approach with piecewise constant interpolations. We discuss issues like numerical stability and efficiency of the implementation.