Page Rank Calculation

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riyad786
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Page Rank Calculation

Beitrag von riyad786 »

Hallo Zusammen,

Can anyone help me to get a little bit info about below formula? I want to know from below picture, What are the PR(t) and C(t) as well as 'd' ?
Bild

And How does this algorithm work? I mean, Final State is showing some value, How to calculate this value?
Bild

Dank im Voraus
riyad

meichholz
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Re: Page Rank Calculation

Beitrag von meichholz »

Hi,

PR(t) is the Page Rank calculated in the previous round of the algorithm (initially 1) and C(t) is the contribution, i.e. how much affects the PR of a page the PR of the neighbors of this page (calculated by the PR divided by the number of neighbors).

Regarding the algorithm, you start with an initial PR of 1 for all pages. Then you compute the contribution of each page. For example, the leftmost page (with final PR of 0.46) has 1 neighbor (= 1 outgoing link), while the page at the bottom (with final PR of 0.73) has two neighbors.

Starting with the leftmost page, for the following example, I'll use the names A, B, C, D (clockwise).
In the first round of the algorithm, the contribution for A is calculated as follows: C(A) = PR / #Neighbors = 1 / 1 = 1.
C(D) = 1/2 = 0.5.

Next, you update the page ranks for all pages. For example, PR(A) is only affected by C(D), so the new PR(A) = 0.15 + 0,85 * 0.5 = 0.575.
After ~12 rounds, you'll get the values shown in the figure.

Best,
Matthias

riyad786
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Re: Page Rank Calculation

Beitrag von riyad786 »

Hallo Matthias,

herzlichen Dank für die Rückmeldung.....
It was a really nice explanation. But one question is that why (cira ~12 round) does it need? Can I finish after 5,6 or any random number? Is there any rules for the round?

Dank im Voraus
Riyad

meichholz
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Re: Page Rank Calculation

Beitrag von meichholz »

Hi,

I don't know whether there are any rules for the number of iterations, but I don't think so. I just used Excel to do the calculations and after 12 iterations the calculated PR was close to the numbers shown in your example.

Best,
Matthias

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