This paper looks inside FolkRank, one of the well-known folksonomy-based algorithms, to present its fundamental properties and promising possibilities for improving performance in tag recommendations. Moreover, we introduce a new way to compute a differential approach in FolkRank by representing it as a linear combination of the personalized PageRank vectors. By the linear combination, we present FolkRank's probabilistic interpretation that grasps how FolkRank works on a folksonomy graph in terms of the random surfer model. We also propose new FolkRank-like methods for tag recommendations to efficiently compute tags' rankings and thus reduce expensive computational cost of FolkRank. We show that the FolkRank approaches are feasible to recommend tags in real-time scenarios as well. The experimental evaluations show that the proposed methods provide fast tag recommendations with reasonable quality, as compared to FolkRank. Additionally, we discuss the diversity of the top n tags recommended by FolkRank and its variants.