1. The PageRank Citation Ranking “Bringing Order to the Web”

2. 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

3. System Anatomy

4. 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

5. 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

6. Ranking Process Initialize PageRank values based on heuristics Initial 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

7. Examples

8. 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

9. 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

10. 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

11. Convergence Scaling Scales well –161 million links require 45 iterations –322 million links require 51 iterations

12. 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.

13. PageRank with Title Search Simple title search with PageRank AltaVista

14. 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