Google Algorithms and Increasing the Number of Pages

Accumulated PageRank of all pages of the web equals the total number of web pages, it follows directly that an additional web page increases the added up PageRank for all pages of the web by one. But far more interesting than the effect on the added up PageRank of the web is the impact of additional pages on the PageRank of actual websites.

To illustrate the effects of addional web pages, we take a look at a hierachically structured web site consisting of three pages A, B and C, which are joined by an additional page D on the hierarchically lower level of the site. The site has no outbound links. A link from page X which has no other outbound links and a PageRank of 10 points to page A. At a damping factor d of 0.75, the equations for the single pages' PageRank values before adding page D are given by

PR(A) = 0.25 + 0.75 (10 + PR(B) + PR(C))
PR(B) = PR(C) = 0.25 + 0.75 (PR(A) / 2)

Solving the equations gives us the following PageRank values:

PR(A) = 260/14
PR(B) = 101/14
PR(C) = 101/14

After adding page D, the equations for the pages' PageRank values are given by

PR(A) = 0.25 + 0.75 (10 + PR(B) + PR(C) + PR(D))
PR(B) = PR(C) = PR(D) = 0.25 + 0.75 (PR(A) / 3)

Solving these equations gives us the follwing PageRank values:

PR(A) = 266/14
PR(B) = 70/14
PR(C) = 70/14
PR(D) = 70/14

As to be expected since our example site has no outbound links, after adding page D, the accumulated PageRank of all pages increases by one from 33 to 34. Further, the PageRank of page A rises marginally. In contrast, the PageRank of pages B and C depletes substantially.