Sometimes I see two "log out" links, like this:
It is always like this on mobile, and on desktop view I see it when looking at my own profile.
On all other pages (other than my own user profile) that I've checked, it appears like this:
This was confusing to me. When there are two "log out" links, I thought that the top one, which is aligned with my profile, would log me out from all sites, and the second one, which is aligned with "Mathematics", would log me out of Mathematics only.
This is, of course, incorrect; both links go to the same page which logs out of all sites in the network.
To make it clearer, there should always be only one "log out" link. Whether it appears aligned with the profile (which is more intuitive in my opinion), or aligned with the site name, it shouldn't be both.