## How to rank pages on the web

### General notes

• The PageRank methodology creates an order criterium for web pages using exclusively the link structure, hence completely independent from the information contained in each web page.
• There are different ordering criteria, other than PageRank, which use the information contained in each web page (such as, identifying location of given search words or criteria), that are used whenever a Google search is performed. However, the PageRank method is still one the main ordering methods and one the reasons contributing to the enormous success of this search engine.
• If one web page includes multiple links pointing towards to a same web page, these are counted as only one link.
• There exist a few difference between the PageRank methodology described here and the way it is, presumably, actually computed. For example:

- web pages that do not exist in Google's database do not have a PageRank defined, hence their links are not taken into account on the computation of the PageRank values of other pages. Note that for a web page to be referenced in Google's database, there should exist a link pointing towards it from an already registered web page;

- links pointing towards web pages that include no other link (or towards web pages that do not exist in Goolge's database) are not taken into account on the computation of PageRank values;

- links from a page to itself are not taken into account.

• Sometimes the PageRank value of a web page is given as a number between $$0$$ and $$10$$. This is not the real PageRank value, but just a measure of its order of magnitude. Indeed, when represented in this way, what is used is in fact, a logarithmic scale. This implies that, for example, increasing from $$5$$ to $$6$$ in such a scale requires a much larger increase on the PageRank value than increasing from $$2$$ to $$3$$. The applet below gives an interpretation of the relation between the true PageRank value and its representation in this logarithmic scale.

(Click on one of the points representing either the true PageRank value, the representation on the logarithmic scale or on the point in the graphical representation and move it around to see how the two scales are related)

You may find in the Internet several web sites that compute the PageRank value of any page, given its web address, in this logarithmic scale. Here are a few examples: