The Damping Factor

The Damping (or Dampening) factor

Simple setup with 5 pages Let's take the same simple set-up that we used when we looked at the initial values: Page1 links to all pages - and all pages link back.

This time, however, we'll also assume that an external page links to Page5 and passes a PageRank of 5. The set-up would look like this on the spreadsheet:

Simple setup with 5 pages
How to specify the simple structure with inbound link

The result can be seen on this spreadsheet. We make 2 observations:

  1. The total PageRank keeps growing for each iteration. The external PageRank we're receiving is is multiplying and replenishing our site.
  2. The PageRank for the individual pages keeps changing - apparently 12 iterations is not enough to calculate the PageRanks for 5 pages.

Assign different damping factor
Set the damping factor to 40%
Now let's try a low damping factor (meaning that the results are much dampened) - like 40% (picture to the left). The result can be seen on this spreadsheet.

This time we observe that:

  1. The PageRank for the individual pages converge much quicker.
  2. The site's total PageRank still grows, but not as much as with the higher damping factor.
  3. The relative PageRanks have changed. Page5 now has a higher PageRank than Page1.

Let's try a high damping factor - meaning that results are less dampened. There's an example with 97% on this spreadsheet.

So the conclusions are:

  1. A low damping factor (= much damping) will make calculations easier. Since the flow of PageRank is dampened the iterations will quickly converge.
  2. A low damping factor (= much damping) means that the relative PageRank will be determined by PageRank received from external pages - rather than the internal link structure.
  3. A high damping factor (= little damping) will result in the site's total PageRank growing higher. Since there is little damping, PageRank received from external pages will be passed around in the system. It will not grow forever though - the maximum limit is Inbound PageRank * d/(1-d).

So which value does Google use then? Nobody outside the Googleplex knows, but the value recommended in the original paper is 85%.