People think about PageRank in lots of different ways. People have compared PageRank to a “random surfer” model in which PageRank is the probability that a random surfer clicking on links lands on a page. Other people think of the web as an link matrix in which the value at position (i,j) indicates the presence of links from page i to page j. In that case, PageRank corresponds to the principal eigenvector of that normalized link matrix.

In the image above, the lower-left document has “nine points of PageRank” and three outgoing links. The resulting PageRank flow along each outgoing link is consequently nine divided by three = three points of PageRank.

Now let’s talk about the rel=nofollow attribute. Nofollow is method (introduced in 2005 and supported by multiple search engines) to annotate a link to tell search engines “I can’t or don’t want to vouch for this link.” In Google, nofollow links don’t pass PageRank and don’t pass anchortext [*]. Read more at www.mattcutts.com