Last month Donald J. Trump told a crowd in New Hampshire that he would happily annoy his wealthy friends if it meant getting big money out of politics. “I have no friends, as far as I’m concerned,” he said. “You know who my friends are? You’re my friends.”

This, of course, was the sort of just-folks gambit that has won Mr. Trump new — or renewed — friends, like Gov. Chris Christie of New Jersey. But there was perhaps some inadvertent truth in the remark. For nearly half a century, Mr. Trump — mogul, actor, incessant boldface name — has labored to portray himself as a charming bon vivant with a limitless supply of popularity. But his actual social circle has a fairly small diameter — even in his hometown, New York.

“Donald has some friends like me, but he’s much more of a homebody than you’d think,” said Richard LeFrak, a fellow real-estate tycoon who has known Mr. Trump for more than 40 years. “He’s very gregarious and has lots of acquaintances. But people that he’s close to? Not so many.”