This is a Masyu puzzle, with a twist. The loop is not required to pass through black circles. But if a black circle is passed through, it still functions like it would in ordinary Masyu.
(Click for larger size
Unrelated to this puzzle: it occurred to me recently that it’s been over a year since the Numberlink solving primer went up, and I haven’t really done any sort of solving guides since then. It’s not for lack of time or desire, but mostly because I have no idea what to write for and what people might want to see. The Numberlink guide itself had been directly inspired from some comments on a recent (at the time) puzzle of mine.
If there’s a type or anything solving-related that you’d like to see a guide for, I’d be happy to hear the request. While there are some things, particularly Latin Square based puzzles, that I have no authority to write on, I think there’s a fair amount I could do.