As the name reflects, a three-way link exchange is a specific kind of reciprocal link exchange among three domains instead of two. Beside this, another popular link exchange methods that are common and popular among webmasters are known as two-way linking.
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In three way link exchange, there must be three different domains taking part in link building. For example, let's say there are there Doamins A, B and C. Site A links to site B and not vice versa. This way, site B only recieve one way links from A and not linking back to it. Similary, site B links to site C and site C links to site A in one direction. Think of it as a triangle formed betweeb A, B and C as shown in the image below.
One of the major benefit of three way links over the other is that in normal two way reciprocal link exchange, you and your link partner directly exchange links with each other and in this case it becomes easy for search engines to figure it out. But in three way link exchange methods, all the links seems natural to search engines and you can get the maximum benifit out from it. To make it further better, webmasters sometimes also try four way or even five way link exchange strategies.