Social tagging, as a novel approach to information organization and discovery, has been widely adopted in many Web 2.0 applications. Tags contributed by users to annotate a variety of Web resources or items provide a new type of information that can be exploited by recommender systems. Nevertheless, the sparsity of the ternary interaction data among users, items, and tags limits the performance of tag-based recommendation algorithms. In this article, we propose to deal with the sparsity problem in social tagging by applying random walks on ternary interaction graphs to explore transitive associations between users and items. The transitive associations in this article refer to the path of the link between any two nodes whose length is greater than one. Taking advantage of these transitive associations can allow more accurate measurement of the relevance between two entities (e.g., user-item, user-user, and item-item). A PageRank-like algorithm has been developed to explore these transitive associations by spreading users' preferences on an item similarity graph and spreading items' influences on a user similarity graph. Empirical evaluation on three real-world datasets demonstrates that our approach can effectively alleviate the sparsity problem and improve the quality of item recommendation.