Simple works best, so no complex numbers here. Just a picture and words.

PageRank is a number. If you put a link from page A to page B, page A will distribute PageRank to page B. Page A's PageRank does not get diluted by linking out, but the links are worth less, in terms of the value of the PageRank, when there are more links on the page A. In other words, the PageRank to the pages page A links to does get diluted but not the PageRank of page A itself.

For example, page A has 5 links and page B has 50 links. Both page A and B have the same PageRank value. The pages receiving links from page A, will get a higher PageRank value then pages receiving links from page B. Why? Because the PageRank of a page can only give off a distributed fraction of its own PageRank. So pages with less links on them, are more profitable in terms of PageRank building.

The picture below is from a Google Image search on "dilution". Its not meant to explain how PageRank is diluted from page to page (it was meant to explain bacterial growth dilution), but I think it works in our case of PageRank dilution.

On the left is the most concentrated form of a colored liquid. Then you see the concentration is diluted as you pan across to the right of the image. Think of these test tubes as pages and the colored liquid as PageRank. As links develop from page A to page B to page C and so on, the PageRank value of those links dilute from the original numeric value. Kind of similar to how dilution works with the image below.

Forum discussion at WebmasterWorld.

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