The PageRank Algorithm

Assume a small universe of four web pages: A, B, C and D. Links from a page to itself, or multiple outbound links from one single page to another single page, are ignored. PageRank is initialized to the same value for all pages. In the original form of PageRank, the sum of PageRank over all pages was the total number of pages on the web at that time, so each page in this example would have an initial PageRank of 1. However, later versions of PageRank, and the remainder of this section, assume a probability distribution between 0 and 1. Hence the initial value for each page is 0.25.

The PageRank Algorithm transferred from a given page to the targets of its outbound links upon the next iteration is divided equally among all outbound links.

If the only links in the system were from pages B, C, and D to A, each link would transfer 0.25 PageRank to A upon the next iteration, for a total of 0.75.

Suppose instead that page B had a link to pages C and A, while page D had links to all three pages. Thus, upon the next iteration, page B would transfer half of its existing value, or 0.125, to page A and the other half, or 0.125, to page C. Since D had three outbound links, it would transfer one third of its existing value, or approximately 0.083, to A.

In other words, the PageRank Algorithm conferred by an outbound link is equal to the document’s own PageRank Algorithm score divided by the number of outbound links L( ).

In the general case, the PageRank value for any page u can be expressed as:

,

i.e. the PageRank Algorithm value for a page u is dependent on the PageRank values for each page v contained in the set B_u (the set containing all pages linking to page u), divided by the number L(v) of links from page v.