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Suppose you have Site 1 that is the only site that links to Site A, Site B and Site C.
Now do a related site search for Site A and it will suggest Site B and Site C, related to B will be A and C, related to C will be A and B.
If you then introduce site 2 that links to sites B and C only, you may find that site A is no longer related.
One of my favourite applications of this feature is for spotting 'artificial' link networks. I'm sure others use it more productively ;)
Hope that makes some sense, I am hopeless at explaining these things.
I often wonder about this. It can be nice to see to whom the people linking to our competitors also link, but we can do this with link: if we spend some time to follow links from those results.
What occupies my thought is whether this could be part of Google's move towards greater theming, assuming they move in that direction.
I think the most plausible theory was that the web is freeform and natural "communities" were formed via interlinking. The rest of the theory goes something like if one site within the community has more inbound links, it is essentially a vote for the site. So if you factor the theory into your algo, you theoretically improve the serps. I saw a PBS show about it! But here we have plumbed the depths of my knowledge! And I realize that there is nothing new in what I say so I'll go climb under a rock now.
Would this help My Favorite Site to be considered to be related to Google and Yahoo?
It would help, but lots of other people would need to link to my favourite site.com on the same page as google/yahoo links.
Is there any evidence that being 'related' has an effect on ranking or Page Rank?
No, being 'related' is a cause of having links (and therefore page rank) but will have no effect on anything, in my opinion.