At first glance, the way Related Searches are generated looks fairly simple - if your page is about widgets, you may get suggestions for "widgets" and "buying widgets". Sometimes the connection doesn't seem quite as obvious, but it looks like a close miss on the page content, or perhaps an overlay of site theme on the page content.
However, I found something a bit surprising. On one page about "widget manufacturing" I found a suggestion for "acme superior widget". That looked odd, and I scanned the text of the page to be sure that "acme" didn't appear anywhere. I checked the SERPs that the link took me to, and the top result was "Acme Superior Widget Manufacturing".
My conclusion was that Google isn't merely extracting key phrases from the page and parroting them back. Rather, it is comparing page content to the RESULTS of other searches and then suggesting a related search. Note that there's no way the the page on my site would have been returned in the suggested search; rather, the top result in the suggested search shared a key phrase with the topic of my page.
(Another thread suggested a related search tie-in with a paid result - in this case, the top result was actually a non-profit site and unlikely to be any kind of advertiser.)
It has done some contextual analysis on your page so google has a pool of adwords its going to use for that page.
I have observed keywords from "Related searches" links and they were scr~wing everything what was to scr~w:
- if banner was about "buy widgets" then keywords from "Related searches" were "get free widgets" - in this way only mentally insane readers would click on "buy" if they can get free.
- if my site was about Macintosh (as example) then keywords from "Related searches" were "buy Windows XP" - in this way readers were being encouraged to buy competitive product
- after clicking on links from from "Related searches" I have seen my main content providing competitors; in other words: clicking on these links could convince some readers to visit the other web sites and not mine, and never come back to mine.
......... so peoplez, please don't call it "contextual analysis" or "complex logic". It was worse than the worst nightmare.
I agree that Related Searches are problematic for the site owner, and I'm delighted they are gone for the moment. But, PolishGuy, was your comment just a rant, or am I missing some information that will help us understand how the displayed searches relate to the page content?