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1) SE's check for all words related to the search words, not just the search words themselves. Is this correct? How do the SE's generate the related world list?
2) SE's check the site as a whole, not just the page which pops up. A site with many relevant pages will therefore do better.
3) For some reason, SE's like things to be divided into that pyramid structure. Why?
Can anyone help?
I'll try to answer this the best I can Franklin.
Some search engines are starting to collect data from multiple queries to figure out the relationship/similarity pattern.
For example, they notice that these searches are very popular:
keyword_a keyword_b
keyword_c keyword_a
keyword_b keyword_c
keyword_d keyword_a keyword_c
keyword_a keyword_d
keyword_b keyword_a keyword_d
All this data will show that keywords(a)(b)(c)(d) have some relation with one another, even though they do not always exist together in search queries.
If a site has all these keywords, it will be determined a better source for any information this search engine recognizes as having a relationship.
Not all search engines will follow through with this unless your site is deemed as a true authority for popular related information. You will usually see this under general type searches. The more specific the search is, the more they will look to specific page.
There are factors other than themes that are calculated and each search engine has it's own methods for ranking. So how well your site is themed does not neccessarily mean it will be regarded as the best source of info on the various subjects. But you are safer having it themed.
2) With most SE's yes.
3)It depends on the SE. Some care. Some don't. Some appear to care because of how the site gets ranked but they don't. For those that care, if a search engine crawls the links on your site, they would not like to find a large amount of totally irrelevant information on pages that are linked to from a topic that is not "generally" similar.