User satisfaction is often dependent on providing accurate and diverse recommendations. In this paper, we explore algorithms that exploit random walks as a sampling technique to obtain diverse recommendations without compromising on efficiency and accuracy. Specifically, we present a novel graph vertex ranking recommendation algorithm called RP3β that re-ranks items based on 3-hop random walk transition probabilities. We show empirically, that RP3β provides accu- rate recommendations with high long-tail item frequency at the top of the recommendation list. We also present approx- imate versions of RP3β and the two most accurate previously published vertex ranking algorithms based on random walk transition probabilities and show that these approximations converge with increasing number of samples.