The PageRank Citation Ranking“Bringing Order to the Web”

Google Design Goals

Scale up to work with much larger collections– In 1997, older search engines were breaking down

due to manipulations by advertisers, etc.

Exhibit high precision among top-ranked documents– Many documents are kind-of relevant– For the Web, relevant should be just the very best

documents

Provide data sets for academic research on search engines

System Anatomy

Basic Concept

Bibliometrics– Use citation patterns like for academic

research– But Web documents are not reviewed– Web documents do not have the same cost

of production/publishing– Programs can easily generate pages pointing

to another page– Very valuable to attempt to game the system

PageRank Design

PageRank– Rank importance of pages– Each incoming link raises importance– Importance increment related to rank of

source page– Importance increment normalized for number

of links on source page

A high ranking results from– Lots of links from low ranked pages– Fewer links from highly ranked pages

Ranking Process

Initialize PageRank values based on heuristicsInitial values do not change results, only time to

converge

Repeat until the rankings converge:For each incoming link L

PageRank = PageRank + Rank ( Source (L) ) #Links ( Source (L) )

Model Web user with some chance of jumping to random location

PageRank = c * PageRank

Examples

Problem with Subgraphs

The Web is composed of many independent graphs – Links among themselves but no links in/out of

the set– This results in ranking between independent

graphs to be difficult

Solution– Introduce a decay factor– This also increases the rate of convergence

Problem with Dangling Links

Many links go to pages with no outgoing links – Influence the distribution of “rank”

• Don’t know how to push their rank back into system during iteration

– They are to pages that• Have no links• Have not been downloaded • Are not in a form that the system can identify

– There are lots of them

Solution– Remove “dead-ends” during convergence– Compute ranks of these after convergence

Implementation

Web issues– Infinitely large Web sites, pages, and URLs– Much broken HTML– Web is constantly changing

PageRank Implementation– Each URL assigned integer ID– Dangling links iteratively pruned from graph

• Few iterations get rid of most– Generate guess at ranking

• Does not affect outcome (much), just how fast it converges– Iterate rank computation until convergence– Add dangling links back in– Iterate rank computation again for the same number

of times that it took for dangling links to be removed

Convergence Scaling

Scales well– 161 million links require 45 iterations– 322 million links require 51 iterations

Searching with PageRank

Google search– Uses a variety of factors

• Standard IR measures• Proximity• Anchor Text• PageRank

– PageRank most valuable for underspecified queries (e.g. few terms, lots of results)

– “Spam pages” given no/low PageRank to reduce their effect on resulting weights.

PageRank with Title Search

Simple title search with PageRank AltaVista

PageRank Applications

Estimating WebTraffic– Because it models a random Web surfer

Backlink Predictor– Like to estimate number of backlinks to identify

important pages• Use CPU/bandwidth to increase precision

– Use incomplete data to rank pages to generate order of importance for crawling

User Navigation– Browser can annotate link based on PageRank to

provide user clue as to destination’s value