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"This president is going to lead us out of this
recovery." - Dan Quayle, at a campaign stop in California
and and then at CA State University, Fresno (The Quayle
Quarterly, Spring/Summer 1992)
What is PageRank?
PageRank is a numeric value that represents how important a
page is on the web. Google figures that when one page links to
another page, it is effectively casting a vote for the other
page. The more votes that are cast for a page, the more important
the page must be. Also, the importance of the page that is
casting the vote determines how important the vote itself is.
Google calculates a page's importance from the votes cast for it.
How important each vote is is taken into account when a page's
PageRank is calculated.
PageRank is Google's way of deciding a page's importance. It
matters because it is one of the factors that determines a page's
ranking in the search results. It isn't the only factor that
Google uses to rank pages, but it is an important one.
From here on in, we'll occasionally refer to PageRank as
"PR".
Notes: can
control which sites they link out to. For this reason, links into
a site cannot harm the site, but links from a site can be harmful
if they link to penalized sites. So be careful which sites you
link to. If a site has PR0, it is usually a penalty, and it would
be unwise to link to it.
To calculate the PageRank
for a page, all of its inbound links are taken into account.
These are links from within the site and links from outside the
site.
PR(A)
= (1-d) + d(PR(t1)/C(t1) + ... + PR(tn)/C(tn))
That's the equation that
calculates a page's PageRank. It's the original one that was
published when PageRank was being developed, and it is probable
that Google uses a variation of it but they aren't telling us
what it is. It doesn't matter though, as this equation is good
enough.
In the equation 't1 - tn'
are pages linking to page A, 'C' is the number of outbound links
that a page has and 'd' is a damping factor, usually set to 0.85.
We can think of it in a
simpler way:-
a
page's PageRank = 0.15 + 0.85 * (a "share" of the
PageRank of every page that links to it)
"share" = the
linking page's PageRank divided by the number of outbound links
on the page.
A page "votes"
an amount of PageRank onto each page that it links to. The amount
of PageRank that it has to vote with is a little less than its
own PageRank value (its own value * 0.85). This value is shared
equally between all the pages that it links to.
From this, we could
conclude that a link from a page with PR4 and 5 outbound links is
worth more than a link from a page with PR8 and 100 outbound
links. The PageRank of a page that links to yours is important
but the number of links on that page is also important. The more
links there are on a page, the less PageRank value your page will
receive from it.
If the PageRank value
differences between PR1, PR2,.....PR10 were equal then that
conclusion would hold up, but many people believe that the values
between PR1 and PR10 (the maximum) are set on a logarithmic
scale, and there is very good reason for believing it. Nobody
outside Google knows for sure one way or the other, but the
chances are high that the scale is logarithmic, or similar. If
so, it means that it takes a lot more additional PageRank for a
page to move up to the next PageRank level that it did to move up
from the previous PageRank level. The result is that it reverses
the previous conclusion, so that a link from a PR8 page that has
lots of outbound links is worth more than a link from a PR4 page
that has only a few outbound links.
Whichever scale Google
uses, we can be sure of one thing. A link from another site
increases our site's PageRank. Just remember to avoid links from
link farms.
Note that when a page
votes its PageRank value to other pages, its own PageRank is not
reduced by the value that it is voting. The page doing the voting
doesn't give away its PageRank and end up with nothing. It isn't
a transfer of PageRank. It is simply a vote according to the
page's PageRank value. It's like a shareholders meeting where
each shareholder votes according to the number of shares held,
but the shares themselves aren't given away. Even so, pages do
lose some PageRank indirectly, as we'll see later.
Ok so far? Good. Now
we'll look at how the calculations are actually done.
For a page's calculation,
its existing PageRank (if it has any) is abandoned completely and
a fresh calculation is done where the page relies solely on the
PageRank "voted" for it by its current inbound links,
which may have changed since the last time the page's PageRank
was calculated.
The equation shows
clearly how a page's PageRank is arrived at. But what isn't
immediately obvious is that it can't work if the calculation is
done just once. Suppose we have 2 pages, A and B, which link to
each other, and neither have any other links of any kind. This is
what happens:-
Step
1: Calculate page A's PageRank from the value of its inbound
links
Page A now has a new
PageRank value. The calculation used the value of the inbound
link from page B. But page B has an inbound link (from page A)
and its new PageRank value hasn't been worked out yet, so page
A's new PageRank value is based on inaccurate data and can't be
accurate.
Step
2: Calculate page B's PageRank from the value of its inbound
links
Page B now has a new
PageRank value, but it can't be accurate because the calculation
used the new PageRank value of the inbound link from page A,
which is inaccurate.
It's a Catch 22
situation. We can't work out A's PageRank until we know B's
PageRank, and we can't work out B's PageRank until we know A's
PageRank.
Now that both pages have
newly calculated PageRank values, can't we just run the
calculations again to arrive at accurate values? No. We can run
the calculations again using the new values and the results will
be more accurate, but we will always be using inaccurate values
for the calculations, so the results will always be inaccurate.
The problem is overcome
by repeating the calculations many times. Each time produces
slightly more accurate values. In fact, total accuracy can never
be achieved because the calculations are always based on
inaccurate values. 40 to 50 iterations are sufficient to reach a
point where any further iterations wouldn't produce enough of a
change to the values to matter. This is precisiely what Google
does at each update, and it's the reason why the updates take so
long.
One thing to bear in mind
is that the results we get from the calculations are proportions .
The figures must then be set against a scale (known only to
Google) to arrive at each page's actual PageRank. Even so, we can
use the calculations to channel the PageRank within a site around
its pages so that certain pages receive a higher proportion of it
than others.
NOTE: added to the page's existing PageRank. The
new value (result + existing PageRank) is then used when sharing
PageRank with other pages. These explanations are wrong for the
following reasons:-
1. They quote the
same, published equation - but then change it
from PR(A) = (1-d) + d(......) to PR(A) = PR(A) + (1-d) + d(......)
It isn't correct, and it
isn't necessary.
2. We will be
looking at how to organize links so that certain pages end up
with a larger proportion of the PageRank than others. Adding to
the page's existing PageRank through the iterations produces
different proportions than when the equation is used as
published. Since the addition is not a part of the published
equation, the results are wrong and the proportioning isn't
accurate.
According to the
published equation, the page being calculated starts from scratch
at each iteration. It relies solely on its inbound links.
The 'add to the existing PageRank' idea doesn't do that, so its
results are necessarily wrong.
Fact:
A website has a maximum amount of PageRank that is distributed
between its pages by internal links.
The maximum PageRank in a site
equals the number of pages in the site * 1. The maximum is
increased by inbound links from other sites and decreased by
outbound links to other sites. We are talking about the overall
PageRank in the site and not the PageRank of any individual page.
You don't have to take my word for it. You can reach the same
conclusion by using a pencil and paper and the equation.
Fact:
The maximum amount of PageRank in a site increases as the number
of pages in the site increases.
The more pages that a site has, the
more PageRank it has. Again, by using a pencil and paper and the
equation, you can come to the same conclusion. Bear in mind that
the only pages that count are the ones that Google knows about.
Fact:
By linking poorly, it is possible to fail to reach the site's
maximum PageRank, but it is not possible to exceed it.
Poor internal linkages can cause a
site to fall short of its maximum but no kind of internal link
structure can cause a site to exceed it. The only way to increase
the maximum is to add more inbound links and/or increase the
number of pages in the site.
Cautions:
Whilst I thoroughly recommend creating and adding new pages to
increase a site's total PageRank so that it can be channeled to
specific pages, there are certain types of pages that should not
be added. These are pages that are all identical or very nearly
identical and are known as cookie-cutters. Google considers them
to be spam and they can trigger an alarm that causes the pages,
and possibly the entire site, to be penalized. Pages full of good
content are a must.
What can we do with this
'overall' PageRank?
We are going to look at some
example calculations to see how a site's PageRank can be
manipulated, but before doing that, I need to point out that a
page will be included in the Google index only if one or
more pages on the web link to it. That's according to Google. If
a page is not in the Google index, any links from it can't be
included in the calculations.
For the examples, we are going to
ignore that fact, mainly because other 'Pagerank Explained' type
documents ignore it in the calculations, and it might be
confusing when comparing documents. The calculator
operates in two modes:- Simple and Real. In Simple mode, the
calculations assume that all pages are in the Google index,
whether or not any other pages link to them. In Real mode the
calculations disregard unlinked-to pages. These examples show the
results as calculated in Simple mode.
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