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Revealing unknown network structure from observed data is a fundamental inverse problem in network science. Current reconstruction approaches were mainly proposed to infer the unsigned networks. However, many social relationships, such as friends and foes, can be represented as signed social networks that contain positive and negative links. To the best of our knowledge, the method of reconstructing signed networks has not yet been developed. To this purpose, we develop a statistical inference approach to fully reconstruct the signed network structure (positive links, negative links, and nonexistent links) based on the Ising dynamics. By the theoretical analysis, we show that our approach can transfer the problem of maximum likelihood estimation into the problem of solving linear systems of equations, where the solution of the linear system of equations uncovers the neighbors and the signs of links of each …