 |
 |
We take a look at our example
web consisting of the pages A, B and C, whereby page A links
to the pages B and C, page B links to page C and page C links
to page A. In this case, the damping factor d is set to 0.75.
So, we get the following equations for the iterative computation
of the single pages' PageRank values: |
|
|
PR(A) = 0.25 + 0.75 PR(C)
PR(B) = 0.25 + 0.75 (PR(A) / 2)
PR(C) = 0.25 + 0.75 (PR(A) / 2 + PR(B))
Basically, it is not necessary to assign starting values to the
single pages before the computation begins. They simply start with
a value of 0 and we get the following PageRank values during the
iterations:
Iteration
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22 |
PR(A)
0
0.25
0.70117
0.92323
1.03253
1.08623
1.11280
1.12583
1.13224
1.13540
1.13696
1.13772
1.13810
1.13828
1.13837
1.13842
1.13844
1.13845
1.13846
1.13846
1.13846
1.13846
1.13846 |
PR(B)
0
1.34375
1.51294
1.59621
0.63720
0.35737
0.66730
0.67219
0.67459
0.67578
0.67636
1.67665
0.67679
0.67686
0.67689
0.67691
0.67692
0.67692
0.67692
0.67692
0.67692
0.67692
0.67692 |
PR(C)
0
0.60156
0.89764
1.04337
1.11510
1.15040
1.16777
1.17633
1.18054
1.18261
1.18363
1.18413
1.18438
1.18450
1.18456
1.18459
1.18460
1.18461
1.18461
1.18461
1.18461
1.18461
1.18462 |
|
|
|
|
If we assign 1 to each page before the computation starts, we get
the following PageRank values during the iterations:
Iteration
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19 |
PR(A)
1
1
1.07031
1.10492
1.12195
1.13034
1.13446
1.13649
1.13749
1.13798
1.13823
1.13835
1.13840
1.13843
1.13845
1.13845
1.13846
1.13846
1.13846
1.13846 |
PR(B)
1
0.625
0.65137
0.66434
0.67073
0.67388
0.67542
0.67618
0.67656
0.67674
0.67684
0.67688
0.67690
0.67691
0.67692
0.67692
0.67692
0.67692
0.67692
0.67692 |
PR(C)
1
1.09375
1.13989
1.16260
1.17378
1.17928
1.18199
1.18332
1.18398
1.18430
1.18446
1.18454
1.18458
1.18460
1.18461
1.18461
1.18461
1.18461
1.18461
1.18462 |
|
|
|
|
If we now assign a starting value to each page, which is closer
to its effective PageRank (1.1 for page A, 0.7 for page B and 1.2
for page C), we get the following results:
Iteration
0
1
2
3
4
5
6
7
8
9
10
11
12
13 |
PR(A)
1.1
1.15
1.14414
1.14126
1.13984
1.13914
1.13879
1.13863
1.13854
1.13850
1.13848
1.13847
1.13847
1.13846 |
PR(B)
0.7
0.68125
0.67905
0.67797
0.67744
0.67718
0.67705
0.67698
0.67695
0.67694
0.67693
0.67693
0.67692
0.67692 |
PR(C)
1.2
1.19219
1.18834
1.18645
1.18552
1.18506
1.18483
1.18472
1.18467
1.18464
1.18463
1.18462
1.18462
1.18462 |
|
|
|
|
So, the closer the assigned starting values are to the effective results
we would get by solving the equations, the faster do the PageRank
values converge in the iterative computation. Less iterations are
needed, which can be useful for providing more up to date search results,
especially regarding the growth rate of the web. Starting point for
an accurate presumption of the actual PageRank distribution may be
the PageRank values of a former PageRank calculation. All the pages
which are new in the index could get an initial PageRank of 1, which
will then be a lot closer to the effective PageRank value after the
first few iterations.
 Next
Article Segment
9.
Additional Factors Influencing PageRank
This article reproduced with permission of eFactory.
© 2002 eFactory Internet-Agentur KG Online-Marketing - written
by Markus Sobek
PageRank and Google are trademarks of Google Inc., Mountain ViewCA,
USA.
PageRank is protected by US Patent 6,285,999.
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