Web Links from the Search Engine's Perspective - Search Engine's View of Web Links
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Before conceptualizing how a search engine views a link, I want to define one more term used often within the search engine company. In diagram 3, you will notice that page B and page C are connected through page A. In other words, there is a "direct edge" between B and C, which is A.

Search engines can view page B and C to be within the same community, or at least assign a lower weight than a direct link between the two pages of the community-like relationship between page B and C.
Link Structure of the Web
Search engines can take a step beyond what humans can compute. They look at the entire Web from a one-way linkage view, triangular linkage view, reciprocal linkage view and a direct edge linkage view.
Envision the three diagrams above multiplied together to form hundreds, if not thousands, of pages with various forms of linkage between them. Now isolate the pages that link in one of the four fashions mentioned above and assign a solid red line to represent a one-way link, a dotted red link to represent a reciprocal link, then mentally note the links that are triangular in nature and finally, I have highlighted the links that are direct edges in yellow/red.
After you have all of that mapped out, stand over this color document and look down. You should be able to quickly see an unnatural linking pattern between groups of pages. For example, look at the page on the second row to the left, second box down. You will see that many dotted red lines point to the box (page). That means there is a lot of reciprocal linking taking place between that page and others. While you are at it, try to locate pages that are linking in triangular patterns versus one way links.

Search engines have the computational power, the algorithmic know-how and the experience to effortlessly find any unnatural linkage scheme. Of course, you need to determine what would be unnatural versus natural. It is very possible for you to naturally have reciprocal links, triangular links and so on. But if you see an "excessive" pattern of one category of the link types mentioned above, then a red flag may be raised.
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