The Pagerank method was founded by Google in order to establish the popularity of sites. Links between sites were based on when creating this method. The topology on the internet was exampled.
The main idea of Page Rank is as such: If site A has published the link of site B, the reason for this is because it was thought that the visitors of page A have most likely visited page B. According to this structure, page A will have increased the pagerank of page B.
But the Pagerank concept is not only limited to this. The two ideas that i have mentioned down below also play an important role in this.
• However high a pagerank page A has, page B's pagerank value will also increase in proportion to that of page A.
• The small amount of outside links that page A has, page Bs pagerank will increase in accordance to this. Based on this logic, if page A sees only page B worthy enough to give links to, page Bs pagerank will increase that much more higher.
After explaining the logic, let us now formulate this system. Before we start let us say that we took this formula from Googles two founders. The formula has changed up till now but the general idea is still the same.
Lets say A1, A2,..., are the pages that give links to page B. And let us say that PR(Ak) is the pagerank of page Ak. Let N(Ak) be the number of links that page Ak gives to outside pages. Let d be the coefficient that changes between 0 and 1 and which is generally 0.85.
In this situation the mathematical value of PageRank is as such:
PR(B)=(1-d)+d x (PR(A1) /N(A1) + ... + PR(An) / N(An) )
You may think this formula is simple and also complicated at the same time. It is simple because its tied to only a few conditions. Its complicated because to calculate this you would have had to calculate the pagerank of another site beforehand.
This is actually quite simple, if you fix all pageranks to a certain value it doesn't seem complicated at all. If you give the same value to all pages; make this value whatever value you want the results will not change.
When you start repeating the formula, the result will be calculated in accordance to the calculation that was made beforehand. As the process progresses the pagerank values will become more settled and there will be no change in between all calculations that are made.
The Random Walking Model
In the calculation of the PageRank value there is another model besides the formula. And this is a model that randomly comes across links on the Internet.
Just think about it, when someone is looking at a page and a link catches their attention, they click on it and start looking at that page. By doing this they will have looked at many pages.
The PageRank value can be dependent on the length of time that a visitor has spent on a site.
If there is a return link on the page that you have visited, this possibility will increase even more. This is where we can discuss the formulas second term.
The first term shows the length of time you may possibly spend before exiting the page you are on. This is actually what we meant by the d symbol in the formula.