In this paper, we consider two particular problems of directed graph matching. The first problem concerns graphs with nodes that have been subdivided into classes of different type. The second problem treats graphs with edges of different types. In the two cases, the matching process is based on a constrained projection of the nodes and of the edges of both graphs in a lower dimensional space. The procedures are formulated as non-convex optimization problems. The objective functions use the adjacency matrices and the constraints on the problem impose the isometry of the so-called projections. Iterative algorithms are proposed to solve the optimization problems. As illustration, we give an example of graph matching for graphs with two types of nodes and graphs with two types of edges
