Comparative analysis is a topic of utmost importance in structural bioinformatics. Recently, a structural counterpart to sequence alignment, called multiple graph alignment, was introduced as a tool for the comparison of protein structures in general and protein binding sites in particular. Using approximate graph matching techniques, this method enables the identification of approximately conserved patterns in functionally related structures. In this paper, we introduce a new method for computing graph alignments motivated by two problems of the original approach, a conceptual and a computational one. First, the existing approach is of limited usefulness for structures that only share common substructures. Second, the goal to find a globally optimal alignment leads to an optimization problem that is computationally intractable. To overcome these disadvantages, we propose a semi-global approach to graph alignment in analogy to semi-global sequence alignment that combines the advantages of local and global graph matching.