The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.