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In this study, the problem of low complexity multiple-input-multiple-out signal detection based on belief propagation (BP) is addressed. The authors propose an edge selection approach that works on factor graph model to cut down the number of circles and high complexity of standard BP algorithm. The message passing from factor nodes to variable nodes is updated by only partial edges, and the mean feedback method is designed to compensate the information loss brought by the edge selection. Both binary and high-order modulations are considered, and the scheme of mapping between bit soft output and modulation symbols when computing the feedback information is discussed. In addition, a minimum mean-square error filter initialised algorithm is proposed, in which the initial message of BP detection is exploited. Both binary and high-order modulations are discussed as well when the authors design this initial message. Simulation results along with convergence and complexity analyses verify that the proposed edge selection approach can achieve good performance with low complexity, and significantly outperform the existing methods with comparative complexity. Moreover, our approach has asymptotic optimality and is a self-adapting scheme, which can achieve the trade-off between performance and complexity by varying the number of selected edges.