# File:PageRanks-Example.svg

Original file(SVG file, nominally 758 × 611 pixels, file size: 33 KB)
Description

Numeric examples of PageRank values in a small graph with a damping factor of 0.85. The exact solution is:

${\displaystyle \mathbf {R} ={\begin{bmatrix}PR(A)\\PR(B)\\\vdots \\PR(K)\end{bmatrix}}={\dfrac {1}{579662461}}\cdot {\begin{pmatrix}19002201\\222822800\\198772220\\22657320\\46886400\\22657320\\9372840\\9372840\\9372840\\9372840\\9372840\end{pmatrix}}\approx {\begin{pmatrix}0,03278149\\0,38440095\\0,34291029\\0,03908709\\0,08088569\\0,03908709\\0,01616948\\0,01616948\\0,01616948\\0,01616948\\0,01616948\end{pmatrix}}}$

And here’s the solution for any arbitrary damping factor d:

${\displaystyle \mathbf {R_{d}} ={\begin{bmatrix}PR_{d}(A)\\PR_{d}(B)\\\vdots \\PR_{d}(K)\end{bmatrix}}=\left({\dfrac {1}{(d+1)\cdot (7\,d^{4}+28\,d^{2}+12\,d-132)}}\right)\cdot {\begin{bmatrix}\left({d}+1\right)\left(7\,{d}^{3}+6\,{d}+12\right)\left({d}-1\right)\\-9\,{d}^{3}-18\,{d}^{2}-46\,{d}-12\\-11\,{d}^{4}-12\,{d}-12-18\,{d}^{3}-32\,{d}^{2}\\2\,\left({d}+1\right)\left(7\,{d}^{2}+2\,{d}+6\right)\left({d}-1\right)\\12\,\left({d}+1\right)\left(4\,{d}^{2}-3\,{d}-1\right)\\2\,\left({d}+1\right)\left(7\,{d}^{2}+2\,{d}+6\right)\left({d}-1\right)\\-2\,\left({d}+1\right)\left(-6+{d}^{2}\right)\left({d}-1\right)\\-2\,\left({d}+1\right)\left(-6+{d}^{2}\right)\left({d}-1\right)\\-2\,\left({d}+1\right)\left(-6+{d}^{2}\right)\left({d}-1\right)\\-2\,\left({d}+1\right)\left(-6+{d}^{2}\right)\left({d}-1\right)\\-2\,\left({d}+1\right)\left(-6+{d}^{2}\right)\left({d}-1\right)\end{bmatrix}}}$
Date 2007-11-25, 2008-01-29
Source en:Image:PageRanks-Example.jpg. Inspired in File:PageRank-hi-res.png.
Author en:User:345Kai, User:Stannered
Permission
(Reusing this file)
 This work has been released into the public domain by its author, 345Kai at English Wikipedia. This applies worldwide.In some countries this may not be legally possible; if so:345Kai grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
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## File history

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Date/TimeThumbnailDimensionsUserComment
current16:17, 8 July 2009758 × 611 (33 KB)FrakturfreundAdded the procent sign for clarity after a discussion in the german wikipedia.
00:19, 29 January 2008758 × 611 (33 KB)Stannered{{Information |Description=Numeric examples of PageRanks in a small system. |Source=en:Image:PageRanks-Example.jpg |Date=2007-11-25, 2008-01-29 |Author=en:User:345Kai, User:Stannered |Permission={{PD-user-en|345Kai}} |other_versions=[[:en:Im
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