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Many link prediction algorithms regarding single-layer social networks have been proposed, and however, how to predict interlayer links in multiplex social networks is still in the initial stage. In fact, the prediction of interlayer links in multiplex networks is of great significance, which is closely related to network security, product recommendation, social network mining, and so forth. Given that many social networks are sparse and the number of the first-order common matched neighbors (CMNs) is very few, it is not sufficient to implement link prediction only based on the first-order CMNs. Moreover, many social networks have scale-free property, leading to the roles of CMNs in link prediction which are significantly different. In doing so, we propose a second-order iterative degree penalty (SOIDP) algorithm to predict interlayer links in multiplex networks, in which the information of the first- and second-order CMNs is …