  Personalized PageRank (PPR) is a traditional measure for node proximity on
large graphs. For a pair of nodes $s$ and $t$, the PPR value $\pi_s(t)$ equals
the probability that an $\alpha$-discounted random walk from $s$ terminates at
$t$ and reflects the importance between $s$ and $t$ in a bidirectional way. As
a generalization of Google's celebrated PageRank centrality, PPR has been
extensively studied and has found multifaceted applications in many fields,
such as network analysis, graph mining, and graph machine learning. Despite
numerous studies devoted to PPR over the decades, efficient computation of PPR
remains a challenging problem, and there is a dearth of systematic summaries
and comparisons of existing algorithms. In this paper, we recap several
frequently used techniques for PPR computation and conduct a comprehensive
survey of various recent PPR algorithms from an algorithmic perspective. We
classify these approaches based on the types of queries they address and review
their methodologies and contributions. We also discuss some representative
algorithms for computing PPR on dynamic graphs and in parallel or distributed
environments.
