We present a general method to improve computation of answer sets by analyzing structural properties of normal logic programs. Therefore we use labeled directed graphs associated to normal programs, which can be utilized to compute answer sets. The basic idea is to detect special subgraphs of those graphs corresponding to structural properties of normal programs and transform them into simpler but equivalent subgraphs by applying graph transformations. It turns out that there is no characterization for these graph transformations in terms of normal logic programs. Surprisingly, nested logic programs provide a semantics for the investigated transformations. In order to demonstrate its practical usefulness, we have implemented our approach in the noMoRe system.