For better or worse, friends and family members can influence your health. If a close friend or spouse quits smoking, you’re more likely to quit, medical experts say. But what if your friends’ friends give up cigarettes? A recent study shows that the influence of social networks extends much further than you might think.

Sheila Jennings and Tom White met a few days ago on the patio at an outdoor cafe in the Adams Morgan neighborhood of Washington, D.C. She opened a pack of cigarettes and asked White, who was seated nearby, if he minded.