> efficiently designed, easily understood (regardless of complexity), surprisingly brilliant, fault tolerant in a clean manner, very insightful on a problem area, etc.
I think your description of elegant is good. One more aspect of elegant is: doing all those things you list here in a manner idiomatic to the language and paradigm you're working in. So for example, regardless of how efficient or easily understood your solution is, if you're using loops and mutation in a functional language, it would rarely be considered "elegant" by experienced people working in that paradigm (that's not to say that loops and mutation aren't very occasionally a good idea in functional languages, but they'd still not be considered elegant).
I think your description of elegant is good. One more aspect of elegant is: doing all those things you list here in a manner idiomatic to the language and paradigm you're working in. So for example, regardless of how efficient or easily understood your solution is, if you're using loops and mutation in a functional language, it would rarely be considered "elegant" by experienced people working in that paradigm (that's not to say that loops and mutation aren't very occasionally a good idea in functional languages, but they'd still not be considered elegant).