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The lifetime of wireless sensor networks (WSNs) is optimized if the traffic within the network is adjusted in a way that all nodes dissipate their energies in a balanced fashion. To balance the energy dissipation, nodes split their flows and these flows are forwarded to different nodes acting as relays. In consequence some nodes have too many incoming and/or outgoing links. In this letter we investigate the impact of limiting the number of incoming and outgoing links of nodes on the network lifetime of WSNs through a Mixed Binary Linear Programming (MBLP) framework. Our results show that the decrease in WSN lifetime is less than 1.0% if the limits on the number of incoming and outgoing links are not lower than three.