Personalized PageRank (PPR) replaces the uniform teleport vector in PageRank with a preference vector $\mathbf{v}$ concentrated on a chosen seed set, so the stationary mass measures proximity to those seeds rather than global importance:

$\mathbf{r} = d\, P^{\top} \mathbf{r} + (1-d)\, \mathbf{v}.$

Jeh and Widom (2003) showed that PPR is linear in $\mathbf{v}$ and can be decomposed and scaled efficiently; Haveliwala (2002) used topic-biased $\mathbf{v}$ vectors for topic-sensitive search. Local PageRank (Andersen, Chung, and Lang, 2006) computes an $\varepsilon$-approximate personalized PageRank vector with an approximate push algorithm whose runtime depends on the support of the output rather than on the total graph size, making PPR practical on large graphs. All three variants share a defining property: scores are stationary distributions of damped random walks, so a node's value reflects the summed mass across all reaching paths, with longer paths damped multiplicatively by $d$.