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Nofollow links attributes do not allow search engine bots to follow link.That means if the website owner is linking back to you with nofollow attributes, it does not pass on link juice. Only Humans will be able to follow the links. Though some time back Google made it clear that they don’t consider nofollow link attributes but weightage of such links are really less. Even though, it’s a good practice to use Nofollow link attribute to those link, where you don’t want to pass link-juice.
Dofollow links allow google (all search engines) to follow them and reach our website. Giving us link juice and a backlink. If a webmaster is linking back to you with this link both Search Engine and Humans will be able to follow you. The best way to give someone dofollow love is allowing keyword in the anchor text. This means when you are linking to any website or page, use the targeted keyword as anchor text.