The rapid growth of wireless networks has led to increasing interest in designing new algorithms that can efficiently reduce the energy consumption of routers and other devices. We present a new formulation of the Network Flow problem that takes into account the energy consumption of the data flows, and reduces the overall network energy expenditure. We introduce an energy model for wireless connections and analyse its validity with real measurements. Then we propose a convex optimization problem that establishes energy constraints on the links, and encourages energy savings that induce sparsity (shut-off of links). We propose several algorithms that can be computed in a distributed fashion for different types of capacity constraints. Finally we justify the sparsity of the solution by using the theory of proximal methods and present simulations for different scenarios. Our algorithms have application both in wired networks as well as in TDMA and 802.11 wireless networks.