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Google's rel=next and rel=prev is to indicate pagination as the help docs explain, it launched in September 2011 to solve the issues with paginated content and what content to rank in search.
But those attributes go in the head of your web page, not in any a-elements on the page.
So you wouldn't include the rel=next or rel=prev in your link code but rather in the head of the pages that they are being used. See the help docs for detailed instructions.
Google's John Mueller said on Twitter that if you did use rel=next in your a-element, Google search wouldn't do anything with it. It will likely just ignore it and treat them as normal links without any rel=anything in them.
No, AFAIK we don't use rel=next on a-elements for anything specific in search.
— John ☆.o(≧▽≦)o.☆ (@JohnMu) October 31, 2017
So when implementing these features, make sure to use them properly - I guess that goes without saying?
Forum discussion at Twitter.
