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The link prediction aims at predicting missing or future links in networks, which provides theoretical significance and extensive applications in the related field. However, the degree of confidence in the prediction results has not been fully discussed in related works. In this article, we propose a similarity confidence coefficient and a confidence measure for link prediction. The former is used to balance the reliability of similarity calculation results, which might be untrustworthy due to the information asymmetry in the calculation, and also makes it easier to achieve the optimal accuracy with a smaller number of neighbors. The latter is used to quantify our confidence in the prediction results of each prediction. The experimental results based on the Movie-Lens data set show that prediction accuracy is improved when the similarity between the nodes is corrected by the similarity confidence coefficient. Second, the experiments also confirm that the confidence degree of the link prediction results can be measured quantitatively. Our research indicates that the confidence level on each prediction is determined by the amount of data used in the corresponding calculation, which can be measured quantitatively.