Ah. Thanks for the clarification. At first I didn't realize you were asking about all of those together.
There isn't a link between the first two and the latter two. The root in intelligent is apparently legere, meaning "to bring together" or "to take up". The gen- root in the other two is found in a whole host of words like gentle, genesis, genus, gender, general, generous, genius. The English form is kin, and is found in kin, kind, kindred, and king. They all trace back to a Proto-Indo-European root meaning "beget" or "produce".