In wireless sensor networks, the interference around the application environment may cause the actual distance between any pair of nodes to fail to be measured accurately. Enclosure graph (EG) model uses this distance between nodes as its weight to construct the topology, which does not fully consider the interference. Consequently it will lead to a large amount of energy consumption induced by the application environment. Even it shortens the survival time. According to the feature of network energy inequality in a wireless sensor network and the defect of EG, we first introduce the adjustable factor of node degree, establish a model of communication metric and a model for the node actual survival time. Then according to the demand of network energy equalization and maximum network lifetime, we quantitatively analyze the network node degree, and achieve its regular pattern. In accordance with this regular pattern and sufficient conditions of function extremum, the maximum node energy consumption and the maximum node actual survival time are deduced. And the corresponding optimal node degree is achieved. Finally, according to the above model, in this paper we propose an energy balance and robustness adjustable topology control algorithm for wireless sensor networks. Theoretical analyses show that this algorithm can guarantee that the network is connected and the link of the network is bi-directionally connected. Experiments show that the network takes advantage of this optimal node degree to obtain the high robustness, thus guaranteeing that the information can be transferred unfailingly. This algorithm can effectively balance the node energy, improve the node survival time, enhance the network robustness, and prolong the network's lifetime.
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