Ambient Intelligence (AmI) provides a vision of the information society where heterogeneous hardware entities are disseminated in the environment and used by intelligent agents to provide ubiquitous applications. To ease the integration of new entities in the system, the application and the underlying hardware infrastructure have to be decorrelated. The aim of our research work is to propose mechanisms for the deployment, automatic configuration and monitoring of applications on an heterogeneous hardware infrastructure. In this paper, we model ambient systems to fulfill this purpose. We propose a graph-based mathematical model for ambient systems. This model allows to use a projection algorithm, extending an existing graph matching algorithm, for the deployment and the automatic configuration of applications on an heterogeneous hardware infrastructure. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).