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When one person in a group begins to feel lonely, the negative emotion can spread to others, increasing everybody’s risk for feelings of loneliness, a new study shows.

In a 10-year study of 5,100 people and their social contacts, researchers tracked feelings of loneliness over time by asking participants how many days a week they felt lonely. What they discovered was that loneliness could be contagious and followed a distinct path as it spread through social networks.

Over time, each additional day of loneliness per week that people experience leads to a little more than one extra day of loneliness per month among those in their social network, according to the article, “ Alone in the Crowd: The Structure and Spread of Loneliness in a Large Social Network,” published in the December issue of The Journal of Personality and Social Psychology. The study was conducted by researchers at the University of Chicago; the University of California, San Diego; and Harvard University.

The average person experiences loneliness about 48 days a year, but having a lonely friend can add 17 days of loneliness annually. By comparison, every additional friend can decrease loneliness by about 5 percent, which translates to about two and a half fewer lonely days a year, the study showed.

The idea that loneliness can be contagious is counterintuitive because we tend to believe that, by definition, lonely people keep to themselves. But the study focused on subjective feelings of loneliness, rather than people who were already socially isolated. The research showed that when feelings of loneliness began to emerge, those feelings were transmitted to others before the person began to sever ties and move away from a social network.

“People can feel lonely even when they’re surrounded by other people,” said Dr. Nicholas A. Christakis, a physician and social scientist at Harvard Medical School and co-author of the book “ Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives.” “The traditional perspective on human emotion is that emotions are an individual experience. But we don’t just have these emotions, we show them. Other people can read them, copy them and internalize them.”

Dr. Christakis said that much like pulling a single thread could unravel a sweater, a lonely person could destabilize an entire social network, spreading loneliness to others before moving to the periphery of the group.

“If you’re lonely, you transmit loneliness, and then you cut the tie or the other person cuts the tie,” he said. “But now that person has been affected, and they proceed to behave the same way. There is this cascade of loneliness that causes a disintegration of the social network.”

The lesson, Dr. Christakis said, is that it is in everyone’s self-interest to pay attention to those on the fringe of a group.

“When we pay attention to the experiences of those at the periphery, when we make an effort to prevent this sad experience of loneliness, then we can stabilize the whole social network by preventing this kind of unraveling,” he said. “We all benefit when we attend to the needs of those at the margins.”