Graph edit distance measures the distance between two graphs as the number of elementary operations (vertex/edge insertion, deletion, substitution) required to transform the first graph into the second one. Such a distance allows to define a metric between graphs and has many applications in the structural pattern recognition framework. However, the complexity of the computation of this distance is exponential in the size of both graphs to be compared. In this technical report, we focus our attention on applications where families of graphs to be considered have a finite set of structures. We then investigate under which relationships between the costs of the different elementary operations, such a priori knowledge may be used to pre compute most of the optimal edit path between any two graphs.