I link to your site with the expectation that you link back to mine.

I guess, but more collectively, so like "We both agree to share a list of websites we link to, and anyone who want to add their site to this list also agree to the same". It used to be popular in music, programming and web development blogs, that much I remember, but I can't say how popular it was at large, the web and the internet was pretty much mostly a geeky thing at the time (around 2000s).