The PageRank Citation Ranking: Bringing Order to the Web¶
Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). The PageRank Citation Ranking: Bringing Order to the Web: Bringing Order to the Web.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Eigenvalue And Eigenvector
- In network science, eigenvector centrality and PageRank read a node's importance from the dominant eigenvector of a link matrix, and spectral clustering uses subordinate eigenvectors to find communities.
This sourcePageRank is the dominant eigenvector (eigenvalue 1) of the link operator; power-iteration convergence is governed by the spectral gap, set via the damping factor.
- In network science, eigenvector centrality and PageRank read a node's importance from the dominant eigenvector of a link matrix, and spectral clustering uses subordinate eigenvectors to find communities.
- Network
- … / instructions → edges: BGP peering / network links / RPC calls / data-flow edges → directed edge: one-way channel / dataflow direction → weighted edge: bandwidth / latency / cost → degree: fan-in + fan-out / connection count → path: route / call chain → cluster: subnet / service mesh → centrality: hub / chokepoint
This sourceSeminal application of eigenvector centrality to web-graph ranking and hub identification.
- … / instructions → edges: BGP peering / network links / RPC calls / data-flow edges → directed edge: one-way channel / dataflow direction → weighted edge: bandwidth / latency / cost → degree: fan-in + fan-out / connection count → path: route / call chain → cluster: subnet / service mesh → centrality: hub / chokepoint
- Random Walk
- In computer science, randomized algorithms walk random paths through state spaces: Markov-chain Monte Carlo samples a target distribution by running a random walk whose stationary distribution is the target; PageRank ranks web pages by the long-run visiting frequency of a random surfer walking the hyperlink graph; random walks on graphs underlie clustering, sampling, and the analysis of randomized search.
This sourceRanks pages by the long-run visiting frequency of a random surfer walking the hyperlink graph — a random walk on a graph.
- In computer science, randomized algorithms walk random paths through state spaces: Markov-chain Monte Carlo samples a target distribution by running a random walk whose stationary distribution is the target; PageRank ranks web pages by the long-run visiting frequency of a random surfer walking the hyperlink graph; random walks on graphs underlie clustering, sampling, and the analysis of randomized search.
- Reputation
- Computer science & distributed systems: Reputation scores aggregate strangers' prior experiences so that parties with no shared history can transact — eBay feedback, web-of-trust key endorsement, and PageRank-style link authority all compute a standing from distributed observations, with PageRank treating an inbound hyperlink as a transferable endorsement of a page's authority, as Page, Brin, Motwani, and Winograd (1999) formalized.
This sourceStanford InfoLab. Formalizes an inbound hyperlink as a transferable endorsement of a page's authority, computing standing as a propagated stock from distributed link behavior.
- Computer science & distributed systems: Reputation scores aggregate strangers' prior experiences so that parties with no shared history can transact — eBay feedback, web-of-trust key endorsement, and PageRank-style link authority all compute a standing from distributed observations, with PageRank treating an inbound hyperlink as a transferable endorsement of a page's authority, as Page, Brin, Motwani, and Winograd (1999) formalized.
Domain-specific¶
- Matrix
- The importance of every page is then the dominant eigenvector of a damped version of this matrix: mixing \(M\) with a small chance of jumping to a page at random gives the Google matrix \(G = dM + \frac{1-d}{N}\mathbf{1}\mathbf{1}^\top\), and the ranking is the vector \(\pi\) satisfying \(G\pi=\pi\), the stationary distribution of that damped walk
This sourceThe report that gives PageRank its eigenvector and random-surfer formulation — 'we want the dominant eigenvector of A... computed by repeatedly applying A', with the ranking read as 'the limiting probability that the random walk will be at that node' — and that damps the recursion to escape rank sinks; it damps with a rank-source term, R' = c(AR' + E), rather than with the closed Google-matrix form, which belongs to the later literature.
Supported in partVerified against the source
- The importance of every page is then the dominant eigenvector of a damped version of this matrix: mixing \(M\) with a small chance of jumping to a page at random gives the Google matrix \(G = dM + \frac{1-d}{N}\mathbf{1}\mathbf{1}^\top\), and the ranking is the vector \(\pi\) satisfying \(G\pi=\pi\), the stationary distribution of that damped walk
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Read against the text for 1 of 5 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:f62c2fe70662 · see in the full table