Internet & Modern Computing (1990–Present)Information Retrieval & Web Algorithms
Google PageRank Algorithm
US 6,285,999Stochastic Link Transition Eigenvector & Random Surfer Centrality
Inventor(s)Lawrence Page
Grant Date2001-09-04
Filing Date1998-01-09
LocationStanford, California
The Foundation of the Modern Internet Search Engine: Larry Page's 1998 patent revolutionized information retrieval by shifting the basis of relevance from simple on-page keyword matching to graph-theoretic link citation analysis. The PageRank algorithm models an idealized random surfer traversing the World Wide Web, calculating the stationary probability distribution of arriving at any given document.
United States Patent & Trademark Archive
Historical Specification & Engineering Broadside
Curated & Restored by Classic Patents (classic-patents.com)
METHOD FOR NODE RANKING IN A LINKED DATABASEStochastic Link Transition Eigenvector & Random Surfer Centrality
US 6,285,999Class: G06F 17/30 (Information retrieval; Database structures)
Inventor(s):Lawrence Page
Origin / Location:Stanford, California
Dates:Filed: 1998-01-09 · Granted: 2001-09-04
Engineering Analysis & Physical Principles
How It Works: Step-by-Step Mechanical & Physical Breakdown
PageRank evaluates the authority of web pages by analyzing the mathematical structure of the hyperlink citation graph across the Internet.
The Core Breakthrough Mechanism
A Markov chain transition matrix models a random surfer clicking links with damping probability d = 0.85 and randomly jumping to any page with probability 1 - d.
Interactive Real-Time Physical Simulation
INITIALIZING THREE.JS WEBGL SIMULATION...
Markov Chain Stationary Distributions & Link Centrality.
Host-Model Telemetry/Computed Readout
Markov Chain Stationary Distributions & Link Centrality
Max Node Centrality
0.455PR[1]
Random Jump Probability
15.0%1-d[1]
Damping Factor (d)0.85
Detailed Component Architecture
1Hyperlink Citation Aggregation
Inbound links act as weighted votes of confidence.
Each citing document distributes its current rank score equally among all outbound links.
2Damping Factor & Random Surfer
Prevents rank sink traps and disconnected graph loops.
Ensures the transition matrix is irreducible and primitive, guaranteeing convergence to a unique stationary eigenvector.
Engineering Principles & Equations
Authored explanation paired with its stated mathematical relationGoverning Equations & Engineering Principles
Stationary Markov Link Transition Eigenvector
Information Retrieval & Web Graph CentralityClaim 1Mathematical Governing Law
Terms:
Plain English DecoderHover or tap any highlighted phrase
The global is the stationary distribution of a random surfer clicking links with across the and teleporting uniformly across .
Stationary PageRank Distribution Vector
Probability vector whose i-th component represents the long-term visitation probability of document i
dimensionless1
Documents with higher stationary probability possess higher global authority and rank higher in search results.
Physical Principle & Engineering Insight
PageRank converts subjective human hyperlinking choices into an objective mathematical eigenvector, turning link topology into collective intelligence.
Historical Context: The foundational search algorithm that powered Google and revolutionized global information retrieval.
Perron-Frobenius Theorem & Stationary EigenvectorsAuthored Principle 1
Stated relation
Because the adjusted transition matrix is stochastic and irreducible, power iteration converges rapidly to the principal eigenvector representing steady-state visitation frequency.
Why It Still Matters
PageRank was the algorithmic engine that built Google, solving web search indexing at planetary scale and defining modern network centrality analysis.
Legal Claims Decoder (1 Numbered Claims)
Compare dense legalistic claims directly with decoded plain-English functional specifications.
Claim #1Independent Master Claim
1/1
Verbatim Historical Legal Text
“A computer-implemented method of assigning an importance rank to nodes in a linked database, comprising: determining a plurality of citing nodes that contain links to a selected node; calculating an initial rank for each citing node; and updating the importance rank of the selected node by summing contributions from each citing node, wherein each contribution is proportional to the citing node's rank divided by its total number of outbound links, and scaled by a damping factor representing a transition probability.”
Plain English Engineering Translation
A method for objectively scoring web documents by treating hyperlinks as weighted votes from citing pages.
Key Protected Innovations:
Hyperlink citation graph modelingDamping factor random surfer simulationEigenvector stationary probability distribution
The Historical Bottleneck
Early search engines indexed web pages solely by keyword density, enabling webmasters to spam results with invisible repeated text.
Why Prior Art Failed
- •Keyword stuffing
- •No concept of editorial authority
- •Manual directory curation could not scale
The Breakthrough Insight
“Academic citation indexing (where citations indicate influence) could be adapted to recursive web hyperlink topologies.”
Patent Wars & Legal Litigations
Vs. Robin Li / RankDexInfringement Challenge
Rival Claim & Defense:
Hypertext link analysis and search engine scoring (US Patent 5,920,859)
Litigation Conflict:
Robin Li filed RankDex in 1997 using outbound link anchor text; PageRank used global eigenvector centrality across all links.
Final Resolution & Judicial Outcome:
Both patents coexisted; Stanford University licensed PageRank exclusively to Google.
Civilizational Impact
PageRank organized the world's information, transforming search from a clumsy directory lookup into an instantaneous global knowledge utility.