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If pages B, C, and D each link only to A, they would each confer a 0.25 PageRank to A. All PageRank

PR( ) in this simplistic system would thus gather to A because all links would be pointing to A.

But then suppose page B also has a link to page C, and page D has links to all three pages. The value

of the link-votes is divided among all the outbound links on a page. Thus, page B gives a vote worth

0.125 to page A and a vote worth 0.125 to page C. Only one third of D’s PageRank is counted for

A’s PageRank (approximately 0.083).

In other words, the PageRank conferred by an outbound link L( ) is equal to the document’s own

PageRank score divided by the normalized number of outbound links (it is assumed that links to spe-

cific URLs only count once per document).

In the general case, the PageRank value for any page u can be expressed as:

That is, the PageRank value for a page u is dependent on the PageRank values for each page v out of

the set Bu (this set contains all pages linking to page u), divided by the number of links from page v

(this is Nv).

PageRank Algorithm Including Damping Factor

The PageRank theory holds that even an imaginary surfer who is randomly clicking on links will

eventually stop clicking. The probability, at any step, that the person will continue is a damping fac-

tor d. Various studies have tested different damping factors, but it is generally assumed that the

damping factor will be set around 0.85.

The damping factor is subtracted from 1 (and in some variations of the algorithm, the result is

divided by the number of documents in the collection) and this term is then added to the product of

(the damping factor and the sum of the incoming PageRank scores).

That is,

or (N = the number of documents in collection)

continued

PR

(

A

) =

PR

(

B

)

PR

(

C

)

PR

(

D

)

L

(

B

)

L

(

C

)

L

(

D

)

++ +

(

)

+

d

1 -

d

N

.

. . .

PR

(

A

) = 1 -

d

+

d

PR

(

B

)

PR

(

C

)

PR

(

D

)

L

(

B

)

L

(

C

)

L

(

D

)

++ +

(

)

. . . .

PR

(

u

) =

Bu

PR

( )

L

( )

PR

(

A

) =

PR

(

B

)

PR

(

C

)

PR

(

D

)

L

(

B

)

L

(

C

)

L

(

D

)

++ .

PR

(

A

) =

PR

(

B

)

PR

(

C

)

PR

(

D

)

2 1 3

++ .

PR

(

A

) =

PR

(

B

) +

PR

(

C

) +

PR

(

D

).

195

Understanding the Role of Links and Linking

13

13 1 8:57 195

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