Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... The goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. In this paper, we consider a simplified architecture where a connection between two routers is represented as a link joining two network equipments. When a connection is not used, both network equipments can be turned off. Therefore, in order to reduce power consumption, the goal is to find the routing that minimizes the number of used links while satisfying all the demands. We first present a study on specific topologies, such as trees and complete graphs, that provide bounds and results useful for real topologies. We model the problem as a linear program and propose a heuristic to solve large instances. We exhibit the gain in terms of number of network equipments (leading to a global reduction of the power consumption) for a set of network topologies: we see that for almost all topologies more than one third of the network equipments can be spared for usual ranges of operation. Finally, we discuss the impact of energy efficient routing on the stretch factor and on fault tolerance.