# A simple structure

## The Spreadsheet - a simple structure

Consider the simple set-up to the left. This structure is already typed into the spreadsheet.

Page1 links to Page2, 3, 4 and 5 - and they all link back to Page1. The set-up is entered like shown below:

 How to specify the simple structure

 The first iteration
The orange column holds the initial values - they are set to 1 and should normally not be changed.

Page1 has 4 other pages linking to it - so it gets a high PageRank in the first iteration.

Each of the pages 2, 3, 4 and 5 has only one inbound link, namely Page1. So each of them get only a quarter of Page1's initial PageRank - plus a little damping (see the description of the the formula).

Notice that the sum of the Page Ranks is 5 - so the average is 1.

 The second iteration
 The values converge
In the second iteration Page1 gets a lower PageRank because the four pages that link to it had a low PageRank in the last iteration. The four pages get a higher PageRank because they are linked to from Page1, which had a high PageRank in the previous iteration.

The results are oscillating - but if you make more iterations, you'll see that the results get closer and closer to a final value - as shown at the right.

Try altering the spreadsheet by making more internal links or adding more pages - and see how the PageRank distributes.

The simple structure concentrates PageRank on the home page more than any other structure does. Page1 has a PageRank that is almost half the site's total PageRank. For each new page that is added to the site, Page1's PageRank will grow by a value close to 0.5(1) whereas the PageRank of the existing sub-pages will drop slightly, because Page1 now must feed more sub-pages.

Next: The pyramid structure.

(1) The exact value is (d-d2)/(1-d2) - where 'd' is the damping factor. For d=0.85 this is equal to 0.459449.