Google PageRank

PageRank is an algorhytm for rating the relevance of web sites designed in 1987 by Larry Page and Sergey Brinn. It is the base of Google search engine.

Algorhytm uses strusture of hypertext links as each other "recommendations"of webpages. The rating is not computed just from number of comming links , but from ranks of recomendating sites too.

If we wanna compute PageRank R(a) of site a, we could use scheme that looks like this:

where Ba is group of all pages linking on a, and Nu is number of links going from u. Basicly every site gives its rank to pages, that it links.

Problems with PageRank computing are closed site structures, on which links goes, but doesn't go out. For example two joined sites with link from outside on one of them would during the computing acumulate and will not release anything. This creates some kind of "trap", that Page and Brin calls "sink". Becouse of this is PageRank even more difficult, becouse it stops this sinks.
If you wanna compute Google PageRank for your site, you need to use Google Toolbar. But it is still not completely exact and it works just with IE or mofo. It looks like this:



PageRank is trademark of Google, Inc. and algorythm is patented (Patent USA 6285999) by Stanford University.

For webmaster is importing just that as height is your PageRank, as big importance gives Google to it. As height is importance, as height is the page placed in search result.Of course thats not the only criterium, Google has about 100 of them. Another advantage is that GoogleBot brows the sites with bigger PageRank more often. Google actualize PageRank in cca 3moths intervals.

We must admit that this is all hust a theory and noone without the deepest employers of Google knows for what purpous exactly PageRank is.

References:
Wikipedia (en)
explanation on JakPsatWeb (cz)
Article about toolbar pagerank (cz)