Energy and spectrum resources play significant roles in fifth generation (5G) communication systems. In industrial applications of the 5G era, green communications are a great challenge for sustainable development of networks. Energy harvesting technology is a promising approach to prolong network lifetime. In energy harvesting networks, nodes may replenish energy from a mobile charger to overcome variations of renewable energy. In this article, energy-rich nodes are stimulated to upload surplus energy to the mobile charger, leading to a bidirectional energy flow. This creates a new paradigm that energy flows coexist with data flows, which gives rise to new problems on controlling the energy flows and the data flows. Software defined networking enables centralized control to optimize flow scheduling. We propose a Software Defined Energy Harvesting Network (SD-EHN) architecture for 5G green communications. In the SD-EHN, the data plane, the energy plane and the control plane are decoupled to support flexible energy scheduling and improve energy efficiency, thus to facilitate sustainability in energy harvesting networks. A scenario with a mobile charger acting as a mobile data collector is presented to introduce an energy trading model in SD-EHN. We use stochastic inventory theory to determine the optimal energy storage levels of the nodes. A Nash bargaining game is proposed to solve the benefit allocation problem for energy trading. Numerical results indicate that SD-EHN optimizes energy utilization and saves energy.