Definition: PageRank is the algorithm that ranked early Google results by treating the web as a single enormous Markov chain. It imagines a "random surfer" clicking links forever and scores each page by the long-run probability the surfer is standing on it. Larry Page and Sergey Brin published it in 1998.
TL;DR: PageRank turned "which page is important?" into a solvable math problem: compute the stationary distribution of a random walk over the web's link graph. Its core insight, that a link is a vote weighted by the voter's own score, still shapes how answer engines assess authority. Build an AI app free →
The Idea in One Sentence
A page is important if important pages link to it.
That sentence is circular, and the circularity is the point. You cannot score a page without already knowing the scores of the pages linking to it. PageRank resolves the loop the way physics resolves an equilibrium: iterate until the numbers stop moving.
A gets links from B and C, which are themselves well-linked, so A scores highest. D links to two pages but nothing links to D, so D scores lowest. A link from a strong page is worth more than a link from a weak one, and a page that links to everything dilutes what each of its links carries.
The Random Surfer
The formal model is a walker on the link graph. At each step the surfer picks a random outbound link from the current page and follows it. Repeat forever. PageRank is the share of time the surfer spends on each page: the stationary distribution of that walk.
THE RANDOM SURFER
-----------------
Step 1: land on some page
Step 2: with probability d (about 0.85)
follow a random link from this page
with probability 1 - d (about 0.15)
teleport to a random page anywhere
Step 3: repeat forever
PageRank(page) = fraction of all steps spent on that page
The teleport step is not decoration. It fixes two failures that would otherwise break the whole computation.
Why the Damping Factor Exists
Without teleportation, the web's link graph is not irreducible or aperiodic, so the walk does not converge to a single answer. Two structures cause the trouble.
| Problem | What it looks like | What teleportation does |
|---|---|---|
| Dangling nodes | A page with no outbound links, so the surfer gets stuck | Teleport out of it |
| Rank sinks | A cluster of pages linking only to each other, hoarding all the score | Bleeds score back to the rest of the graph |
Setting the damping factor d to about 0.85 means the surfer follows links 85% of the time and jumps randomly 15% of the time. That small leak guarantees the chain is irreducible and aperiodic, so a unique stationary distribution exists and the iteration converges.
This is a good example of a theoretical condition having a directly practical consequence. The 0.15 is there because the math requires it, not because anyone measured human browsing.
How It Is Computed
PageRank is the stationary distribution of a matrix with billions of rows, which is far too large to solve directly. It is computed by repeated multiplication instead.
- Start every page with an equal score.
- Each page distributes its current score evenly across its outbound links.
- Each page's new score is the sum of what it received, plus the teleport term.
- Repeat until the scores stop changing meaningfully.
This is the power iteration method, and it converges quickly enough to run over the whole web. It is also exactly what you would do to find the stationary distribution of any Markov chain: multiply the state vector by the transition matrix until it stops moving.
What PageRank Was and Was Not
PageRank has been persistently misunderstood, in two directions.
- It was never the whole ranking. Even in 1998 it was one signal combined with text relevance. Modern search uses a very large number of signals, and PageRank is a small, quiet part of a much bigger system.
- The public toolbar number is long gone. The visible 0-to-10 PageRank score was retired years ago. Third-party "authority" metrics are estimates from other people's crawls, not Google's number.
- The paper's insight outlived the specific formula. The durable contribution is treating a link graph as a Markov chain and reading importance off the stationary distribution. That technique now appears far outside search.
| Domain | What the "pages" are | What a "link" means |
|---|---|---|
| Academic citation | Papers | One paper cites another |
| Social networks | People | One person follows another |
| Biology | Proteins | Two proteins interact |
| Road networks | Intersections | A road connects them |
| Recommendations | Items | Users engaged with both |
What Replaced It for AI Search
Answer engines do not rank ten links; they synthesize a response and cite a few sources. Link-graph authority still matters as an input, but the retrieval path is different. A page now has to be extractable as well as authoritative: chunked cleanly, answer-first, and unambiguous when a passage is lifted out of context.
That shift is why answer engine optimization exists as a distinct practice from classic link building. PageRank asked "who vouches for this page?" An answer engine also asks "can I quote a paragraph of this page and be correct?"
The Same Math on Your Own Data
The PageRank technique is not really about the web. It is about ranking anything by flow through a graph, which is a question most teams have and rarely answer.
Describe the tracker to Taskade Genesis: "a board of our accounts showing which ones refer others, and how many downstream accounts each referral chain produced." Taskade EVE builds it as living software on your projects, and an automation keeps the graph current as new records arrive. You get the same "importance flows along edges" reading without writing an eigenvector solver.
Related Concepts
- Markov Chain: the model PageRank is an instance of
- Monte Carlo Method: estimating the same walk by sampling
- Answer Engine Optimization: what authority means for AI search
- Knowledge Graph: another structure where edges carry meaning
- Semantic Search: retrieval by meaning rather than by link
- Information Theory: the other math under search
- Foundations: the rest of the theory under modern AI
Frequently Asked Questions About PageRank
What is PageRank in simple terms?
PageRank scores a web page by imagining someone clicking random links forever and measuring how often they land on that page. A link from a highly-ranked page counts for more than a link from an obscure one.
How does PageRank actually work?
It treats the web as a Markov chain and computes the stationary distribution of a random walk over it, using repeated matrix multiplication until the scores converge. Each page passes its score evenly to the pages it links to.
What is the damping factor?
The probability, conventionally about 0.85, that the random surfer follows a link rather than jumping to a random page. The 15% teleport chance prevents the walk from getting stuck in dead ends or self-referential clusters, which is what guarantees the computation converges.
Does Google still use PageRank?
Google has confirmed PageRank remains one signal among many, but the public toolbar score was retired long ago and it is a small part of a much larger ranking system. Third-party "authority" scores are estimates from other crawls, not Google's internal number.
Who invented PageRank?
Larry Page and Sergey Brin at Stanford, published in 1998. It is named after Larry Page, not after web pages, though the pun is convenient.
What is a rank sink?
A group of pages that link only to each other, accumulating score without passing any back to the wider graph. The damping factor's random teleport is what prevents rank sinks from absorbing all the score.
Is PageRank only useful for web search?
No. The technique ranks importance in any graph: citation networks, social graphs, protein interaction networks, road networks, and recommendation systems all use variants of it.
How does PageRank relate to AI search engines?
Link authority is still an input, but answer engines synthesize responses rather than ranking links, so extractability matters too. A page needs to be quotable and self-contained, which is what answer engine optimization addresses.
Further Reading
- Markov Chains Explained: PageRank in its wider mathematical context
- Answer Engine Optimization: how AI search assesses sources
- Foundations: the rest of the theory under modern AI
- Markov Chain: the parent concept