In cloud computing, instead of building their own network and facilities, companies can allocate resources from network operators, thus reducing hardware investment and maintenance cost. The company's IT infrastructure can be designed as an abstract virtual graph of services to be mapped into the substrate network of the operator. In this paper, we refer to the virtual graph mapping problem as service composition. How to identify and locate the substrate components to map the virtual graph to in an optimal way is the subject of this paper. We propose three algorithms for three different graph topologies: path, star, and tree, whose complexity is O(V 3) + O(E R V 2) where V is the set of substrate network nodes and E R is the set of virtual links. We also provide simulations to evaluate the performance of our algorithms.