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This subject particulary interests me because I am interested in developing a Web site which would by its nature contain very many links to pages found on external sites. I am now worried that my site would, in S.E.O. terms, be like a bucket with a hole in it!
Are my concerns justified?
[edited by: martinibuster at 10:08 pm (utc) on Aug. 22, 2004]
[edit reason] Edited for specifics [/edit]
Maybe one should just link out when it makes sense to the users.
Yes, but in doing so it helps to try to understand all the effects on one's pages, then one is making an informed judgement, and is also able to "optimise" (getting to hate that word) whatever link structure is under one's control (plus it's quite interesting!).
If a page has no outgoing links, a dead end, it has X PR.
If that same page adds a link to www.sustefdtrstfbicuehsj.com, the page will have the exact same PR as if it had no links.
We agree perfectly. If you have a page without outbound links you're committing the Capital Sin of SEO. If you had linked your page to any internal page, you could have increased the site's total PageRank by X*d/(1-d) - i.e. 5.6666 as much.
If you are linking non-reciprocally (e.g.: to www.sustefdtrstfbicuehsj.com) you are still "losing your opportunity to increase PageRank" - but you are passing that opportunity on to the other site. Therefore your PageRank leak / lost opportunity is the same as the new site's increased PageRank.
This leads to Hagstrøm's first law:
For every increase in PageRank, there is an equal and opposite PageRank leak.
You could also suffer the same PageRank leak / lost opportunity by linking to a non-existing page on your own site. I call this an "internal PageRank leak" - leading to Hagstrøm's second law:
There is not an equal and opposite increase in PageRank for
every PageRank leak.
Again, this is extremely simple and should not be made unduly complex. Perhaps the easiest way to understand it is this... if the above mentioned page has one single link off of it which goes to the root source of its PR, that is ideal from a PR standpoint. (Other linking structures could also be ideal, like linking to two pages that link to the page.)Any linking that is not this ideal is simply that, not ideal for the PR of the page in question.
It's even simpler than this: Any internal linking structure will increase your PageRank by 5.6667 - as long as you don't have dead-ends.
I hope this answers Patrick's questions as well :)
Case 1: a one-page site with no outgoing links has a raw PR of 0.15. If it links out, its PR stays the same.
Case 2: a two-page site with both pages linking to each other has a combined raw PR of 2.00 divided equally between the two pages, so they each have a raw PR of 1.00.
Case 3: a two-page site with both pages linking to each other but one links out creates a leaking bucket - a combined loss of PR for those 2 pages. They end up with a combined total of 0.77 - a "leak" of 1.23 (I needed a calculator for that). The page that links out has a PR of 0.43 and the other one has 0.33. The outside page that was linked-to gains 1.23 x 0.85 = 1.05.
Is this correct?
Patrick's First Personal Law is Always Use a Calculator.
And thanks steveb and Hagstrøm. I'm getting there!
Case 3: a two-page site with both pages linking to each other but one links out creates a leaking bucket - a combined loss of PR for those 2 pages. They end up with a combined total of 0.77 - a "leak" of 1.23 (I needed a calculator for that). The page that links out has a PR of 0.43 and the other one has 0.33.
Precisely.
The outside page that was linked-to gains 1.23 x 0.85 = 1.05..
It gains 1.23 (goes from 1 to 2.23) provided that there is a linking structure on the receiving site (in theory, if the page links to itself it will be enough)
Notice that this gain (1.23) is far smaller than the formula I gave ( d/(1-d) ). That's why I wrote that the formula showed the maximum gain. This is one of the really weird aspects of the formula - namely that the amount by which you can increase the PageRank of the linked-to site is determined by the linking structure of the linking site.
It gains 1.23
Isn't there an 85% dampening factor that reduces the amount of PR passed on?
Isn't there an 85% dampening factor that reduces the amount of PR passed on?
I thought you had used the calculator to calculate the PageRank increase? If the linked-to site is a single page, which links to itself, its PageRank will grow from 1 to 2.23.
This means that the PageRank increase (1.23) is equal to the PageRank leak that you yourself calculated (compare with Hagstrøm's First Law), and it also means that the total raw PageRank for these 3 pages will still be exactly 3.
Assuming no other links that is correct. The average PageRank for all the pages in the Google index is 1.0. It is a probability distribution. This also implies that adding pages to Google dilutes the PageRank of existing pages within the index.
If you take your mini-site of two cross-linked pages you effective have a PageRank of 2.0 to spend, if you now add a single link out, some of this PageRank is spent on an external site and the PageRank of the internal pages will fall to 0.43 and 0.33.
I thought that if two pages linked to each other their combined PR would go to 2.00 instead of the 0.30 they would add up to if they didn't interlink.
Perfectly correct.
So there is no dampening factor at play there.
Oh yes there is. But don't forget that "(1-d)" is added to the sum:
PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))Page1 passes all of its PageRank (i.e. 1) to Page2. This PageRank is damped by 85% (or whatever) so Page2 receives only 0.85. Then
(1-d) = (1-0.85) = 0.15The third page - which I have in my mind as an "outside" page (which is probably a wrong concept, as all pages are independent of each other even on the same domain) - I thought would only receive 85% of what an internal page would have.
That is true - for the first iteration. Page3 receives half of Page1's PageRank damped by 0.85, so it's increased by 1 / 2 * 0.85 = 0.425.
So after the first iteration, Page3 has a PageRank of 1.425. If Page3 is a part of a greater site, it can link to other pages on its site (or theoretically, link to itself). This means that in the second iteration, other pages on this "outside site" will have a higher PageRank and they in turn link to other pages on the site in the third iteration and so on.
I thought there was that wastage factor each time a page links to an outside one, though I must be wrong there (and bear in mind that I am not good with figures).
In the first iteration, the passed PageRank will be dampened, so the PageRank that the "outside site" receives from Page1 (one out of two links) is as we just calculated
0.5 * 0.85 = 0.425In the second iteration Page1 will still pass PageRank, but to this we must add the PageRank that Page3 received in the last iteration and which it now passes on to the rest of its site. This "old PageRank" is dampened twice:
0.5 * 0.85 + 0.5 * 0.85 * 0.85 = 0.78625In the third iteration Page1 will still pass PageRank, and we must add the PageRank that the site received in the two previuos iterations and which is now dampened twice and thrice:
0.5 * 0.85 + 0.5 * 0.85 * 0.85 + 0.5 * 0.85 * 0.85 * 0.85 All this is hard to describe, but there's a visiual walk-through on the site in my profile. The sum of these smaller and smaller entities add up to
0.5 * 0.85 / (1 - 0.85)There is one snag in this formula though (and this is why I was waiting for Doc_Z to turn up :) ) - it doesn't take into account the fact that old site is leaking, so the PageRank that Page1 can pass to the "outside site" becomes lower and lower. This is why the actual result will be lower than X * d / (1-d).
Absolutely. Makes perfect sense. But it may determine whether the link is a javascript link or a straight link.
Just a few remarks:
- 'Hagstrøm's first law' is a direct consequence from the fact that the average PR is one. Therefore, the law is only valid for systems without dead ends.
- Indeed, the 'wasted PR' is PR_transferred /(1-d). And in the example of msg #64 you get PR_link_page / 2 * d / (1-d) = 1.23 as expected.
- As far as I know it's not clear if self links are counted or not.
- The PR formula has nothing to do with iterations, i.e. you can solve the linear equations directly within one step. Iterations are only a simple numerical way to receive the solution.
'Hagstrøm's first law' is a direct consequence from the fact that the average PR is one.
That is correct.
Therefore, the law is only valid for systems without dead ends.
Beg to differ. Dead ends / wasted PageRank are covered by Hagstrøm's second law: "There is not an equal and opposite increase in PageRank for every PageRank leak".
This unfortunately confuses the main issue for many people. Pagerank is page based, not domain. "Any internal linking" will benefit the domain equally, but not necessarily the *page* in question.
When a new page, page15, is created on domain.com/, and the only link to page15 is from the main page of domain.com/, the ideal linking in terms of the PR for page15 is to have one single link back to domain.com/. If instead page15 links to ten of the pages on the domain.com site, including the domain.com/ root, then the pagerank for page15 will be less... because it sends less PR to its PR source, and more PR to other pages that disperse PR to other pages, not page15.
Understanding how linking effects the pagerank of a *page* is not exactly the same as understanding how it effects a domain, or the total sum of pages (many domains) under your control. Using PR on a domain should be concerned more about "leaks" to contact, terms and conditions, and other useless-for-search-ranking pages.
That is all a different issue, and should not be confused with the central concept here. The PR of a *page* is maximized by linking (always at least once) to the page or pages that return the most PR back to the original page.
Suppose new page31 has two links pointing to it, from page5 and page7. What is the best linking to maximize page31's PR. If page5 and page7 have the exact same linking, then linking to one or both would be equally fine. But if page5 has four links on it while page7 has eighty links on it, then to maximize the PR of page31, you should only link to page5.
Again, it is a very simple concept. If you only care about PR (which of course is silly), then you should send PR to the page that sends you back the highest percentage of PR. That is for a page. If you care about the total PR of the domains under your control, you have a more complicated issues to juggle, but the basic idea is the same... to maximize your PR, send PR to where you get PR.
