# Google's Page Rank--The Final Product

DevFeed: [Google's Page Rank--The Final Product](<https://devfeed.tech/articles/google-s-page-rank-the-final-product-40206.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/06/20/googles-page-rank-the-final-product/>)

Published: 2011-06-20T22:07:41Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Google](<https://devfeed.tech/topics/google.md>), [Matrix](<https://devfeed.tech/topics/matrix-org.md>), [math](<https://devfeed.tech/topics/math.md>), [Web](<https://devfeed.tech/topics/web.md>)

Tags: [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [google](<https://devfeed.tech/tags/google.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [page-rank](<https://devfeed.tech/tags/page-rank.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [programming](<https://devfeed.tech/tags/programming.md>), [pseudocode](<https://devfeed.tech/tags/pseudocode.md>), [ranking](<https://devfeed.tech/tags/ranking.md>), [search-engine](<https://devfeed.tech/tags/search-engine.md>), [web](<https://devfeed.tech/tags/web.md>)

## AI overview

This article explains how PageRank addresses dangling nodes and non-unique rankings. It introduces positive column-stochastic matrices and the Perron-Frobenius Theorem, then uses random web surfing as a probability-based intuition for webpage importance.

## Source excerpt

Dangling Nodes and Non-Uniqueness Recall where we left off last time. Given a web $ W$ with no dangling nodes, the link matrix for $ W$ has 1 as an eigenvalue, and if the corresponding eigenspace has dimension 1, then any associated eigenvector gives a ranking of the pages in $ W$ which is consistent with our goals. The first problem is that if there is a dangling node, our link matrix has a column of all zeros, and is no longer column-stochastic.