Formal Sciences

Computer Science

1998

Advanced

PageRank Equation

PR(p_i) = \frac{1-d}{N} + d \sum_{p_j \in M(p_i)} \frac{PR(p_j)}{L(p_j)}

Ranks web pages by importance based on the quality and quantity of links pointing to them.

By Larry Page, Sergey Brin

Formal Sciences

PageRank Equation

1998 · Larry Page

Human Reviewed

84%

Rabbit Hole Mode

Five doors into the universe behind this equation. Choose your path.

Story PortalWho discovered this?Discover how Larry Page and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — web search.Math PortalWhat does it derive from?Trace the mathematical lineage from shannon entropy.Future PortalWhere is it going?Knowledge graph reasoning

Why it matters: Transformed how humanity accesses information and pioneered graph-based ranking.

Discoverers: Larry Page, Sergey Brin (1998)

What does it mean?

Ranks web pages by importance based on the quality and quantity of links pointing to them.

Why should I care?

Transformed how humanity accesses information and pioneered graph-based ranking.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$PR(p_i)$	PageRank	—	Importance score of page i
$d$	Damping factor	—	Typically 0.85
$L(p_j)$	Out-links	—	Number of links from page j

Worked Example

A page linked by high-PR pages with few out-links receives more rank.

AI Guide (Pro)

Ask questions about equations and get answers grounded in the Equation Universe catalog.

Upgrade to Pro Try demo (7 days)

Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

Equation Universe