We consider the delay minimization problem in an energy harvesting communication network with energy cooperation. We investigate the problems of optimal energy management at each node and optimal energy routing between nodes through energy cooperation. For the case without energy cooperation, each node needs to distribute its harvested energy over its outgoing links. For this problem, we show that each node should allocate more power to links with more noise power and to links through which more data flow. For the case with energy cooperation, each node needs to distribute its harvested energy among its outgoing links, and in addition, each node may transfer a portion of its harvested energy to neighboring nodes through energy cooperation. For this problem, we develop an iterative algorithm to determine the optimal energy routes in the network. We numerically observe that energy is routed from nodes with lower data loads to nodes with higher data loads.