File:PageRanks-Example.svg

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

\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)
PD-icon.svg This work has been released into the public domain by its author, 345Kai at the English Wikipedia project. This applies worldwide.

In case this is not legally possible:
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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en:Image:PageRanks-Example.jpg, stricter copy of original image

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Date/TimeThumbnailDimensionsUserComment
current16:17, 8 July 2009Thumbnail for version as of 16:17, 8 July 2009758 × 611 (33 KB)Frakturfreund (talk | contribs) (Added the procent sign for clarity after a discussion in the german wikipedia.)
00:19, 29 January 2008Thumbnail for version as of 00:19, 29 January 2008758 × 611 (33 KB)Stannered (talk | contribs) ({{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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