Recommender systems aim to identify relevant items for particular users in large-scale online applications. The historical rating data of users is a valuable input resource for many recommendation models such as collaborative filtering (CF), but these models are known to suffer from the rating sparsity problem when the users or items under consideration have insufficient rating records. With the continued growth of online social networks, the increased user-to-user relationships are reported to be helpful and can alleviate the CF rating sparsity problem. Although researchers have developed a range of social network-based recommender systems, there is no unified model to handle multirelational social networks. To address this challenge, this paper represents different user relationships in a multigraph and develops a multigraph ranking model to identify and recommend the nearest neighbors of particular users in high-order environments. We conduct empirical experiments on two real-world datasets: 1) Epinions and 2) Last.fm, and the comprehensive comparison with other approaches demonstrates that our model improves recommendation performance in terms of both recommendation coverage and accuracy, especially when the rating data are sparse.