How big is a one-degree group?

In 1967, psychologist Stanley Milgram began a series of investigations about the small world phenomenon. Milgram and his collaborators had people attempt to get a letter to a final recipient by sending it to a friend who was, in turn, likely to be friends with the final recipent. Each person in the chain proceeded likewise until the letter was delivered to the final recipient. Milgram found that the separation between two randomly selected Americans in this way is about 6 "hops". His experiment recently got me thinking of a related question:

Pick a group of people who live in NYC whose members collectively know everyone else who lives in NYC. What's the smallest number of people you'd need for that group?

For the purposes of answering the question without resorting to loopholes, let's assume that brand new arrivals (in town less than 3 months) don't count and that "know" means that each person considers the other an acquaintance...that is, something more than just someone they recognize or see daily. Any guesses as to the smallest group size? Better yet, is there any research out there that specifically addresses this question? Or is it impossible...are there people living in the city (shut-ins, hermits) who don't know anyone else? I'll share my best guess in the comments.