Personalized PageRank (PPR) is the seed-specific generalization of PageRank introduced by Jeh and Widom (WWW 2003). The random surfer follows an outgoing edge with probability $1-\alpha$ and teleports with probability $\alpha$, but the teleport distribution is replaced by a user-specified preference vector $\mathbf{r}$ over the nodes, so the resulting stationary score $\boldsymbol{\pi}_{\mathbf{r}}$ concentrates near the seeds in $\mathbf{r}$ rather than spreading uniformly across the graph. Formally, $\boldsymbol{\pi}_{\mathbf{r}}$ is the unique solution of $\boldsymbol{\pi}_{\mathbf{r}} = (1-\alpha)\, P^{\top} \boldsymbol{\pi}_{\mathbf{r}} + \alpha\, \mathbf{r},$ where $P$ is the row-stochastic transition matrix of the graph. The paper also introduces a hub decomposition and dynamic-programming scheme that lets many such personalized vectors be computed at web scale by combining a small set of precomputed partial vectors with a basis of hub vectors. A truncated variant restricts the computation to the highest-weight entries (or bounds the iteration depth), trading recall for compute and yielding the truncated personalized PageRank commonly used as a graph-retrieval baseline.