PageRank

PageRank is fundamentally based on the Random Surfer Model, which imagines a user who starts on a random page and either clicks a link to another page or teleports to a completely new URL. The damping factor (typically set to 0.85) represents the probability that the surfer will continue clicking links rather than jumping to a random page. This stochastic process models realistic browsing behavior and ensures the algorithm converges to a stable probability distribution across the entire web graph.

In the PageRank model, a hyperlink from page A to page B is interpreted as a vote of confidence cast by A for B. However, not all votes are equal. The weight of the vote is proportional to the PageRank score of the voting page itself. A link from a high-authority page like a major research university passes significantly more ranking power than a link from an obscure personal blog. This recursive weighting creates a virtuous cycle where pages linked from important sources become important themselves.

PageRank is computed using an iterative power method algorithm. The calculation begins by assigning an equal score to every page in the index. The algorithm then repeatedly redistributes rank across the link graph until the values stabilize within a small tolerance threshold. For the massive scale of the web, this typically requires dozens of iterations. The final stationary distribution represents the principal eigenvector of the normalized link matrix, guaranteeing a unique and stable ranking vector.

The damping factor is a critical parameter that prevents rank sinks and ensures mathematical convergence. Without it, pages with no outbound links would trap all the rank flowing into them. The standard value of 0.85 means that at each step, there is a 15% probability the random surfer will teleport to any page uniformly. This teleportation vector can be modified to create Personalized PageRank, biasing the random jump toward a specific set of trusted seed pages for custom authority scoring.

A rank sink occurs when a set of pages link to each other but have no outbound links to the rest of the graph, accumulating rank without distributing it. PageRank solves this through the teleportation mechanism inherent in the damping factor. Pages with zero outlinks are treated as if they link to every page in the corpus equally, preventing them from hoarding score. This ensures that the total PageRank in the system remains conserved and that no artificial dead-ends distort the global ranking.

PageRank is a query-independent or static ranking signal, meaning it is computed once for the entire web graph offline and does not depend on the user's search terms. This contrasts with query-dependent signals like TF-IDF or BM25. The pre-computed PageRank score is combined with hundreds of other relevance signals at query time to produce the final search ranking. This static nature allows Google to serve results with extremely low latency, as the authority score is already calculated before any search is performed.