The Math Behind PageRank

anaesthetica writes "The American Mathematical Society is featuring an article with an in-depth explanation of the type of mathematical operations that power PageRank. Because about 95% of the text on the 25 billion pages indexed by Google consist of the same 10,000 words, determining relevance requires an extremely sophisticated set of methods. And because the links constituting the web are constantly changing and updating, the relevance of pages needs to be recalculated on a continuous basis."

Comments

10,000 words

[ambivalentduck]

But 9,000 of those words are slang for parts of the human anatomy.  Go figure.

Bad summary

[Knights who say 'INT]

The article specifically says the PageRank eigenvector is only recalculated once a month, approximately. Even though Google uses some clever numerics to calculate the eigenvectors to a 25 billion by 25 billion matrix by iteration, it still takes several hours to finish.

Pagerank

[Skythe]

Because about 95% of the text on the 25 billion pages indexed by Google consist of the same 10,000 words, determining relevance requires an extremely sophisticated set of methods.

They use a set of nested if-else statements
*ducks*

Re:I joke a lot on Slashdot, but serious question

[Anonymous Brave Guy]

The underlying idea behind page rank is pretty well-exposed at this point, and is described in TFA. Essentially, it's a big set of simultaneous equations: each incoming link to your page gets a score that is roughly the rank of the source page divided by the number of outgoing links on that page, and then the rank of your page is roughly the sum of the scores of all incoming links.

Various fudge factors are introduced along the way. For example, if you break Google's rules about displaying the same content to bots as to humans, you can get slapped right down. More subtly, newly registered domains take a modest hit for a while. More nobody-knows-ly, Google's handling of redirects is unclear: information about exactly what adjustments are made is pretty scarce, and there's a lot of conjecture around. One thing that's pretty certain is that they penalise for duplicate content, which is why some webmasters do apparently unnecessary things like redirecting http://www.theircompany.com/ to http://theircompany.com/ or vice versa.

So, if you want to get a page with a high rank yourself, then ideally you need would get many established, highly-ranked pages to link to your page and no others. In your example, all those Geocities sites wouldn't help a lot, because (a) they'd have negligible rank themselves, and (b) they'd be penalised for being new and lose some of that negligible rank before they even started. Many times negligible is still negligible, and so would be your target page's rank. OTOH, get a few links from university sites, big news organisations and the like, and your rank will suddenly be way up there. Alternatively, get a grass-roots movement going where a gazillion individuals with small personal sites link to you, and the cumulative effect will kick in.

Re:Pagerank is cool

[silentounce]

Interestingly enough, google thinks so, too.

Of course, yahoo has its own opinion.
 
Although, altavista seems to almost agree. Check the second non-advertised result.
 
I do find this amusing though. Third place, how humble.
 
I didn't expect such interesting results. The site with the search term in its url was tops for av and yahoo, but not google. Yahoo ranked the wiki entry above google, but av reversed that decision, google of course thought itself was more important than the wiki. Google's own reference site was number one in its own search and near the top in the other two, but pagerank.net wasn't even in the top 10 for google's search. I'm not sure what conclusions can be drawn from all that, but it is definitely food for thought.