Nicholas A. Christakis & James H. Fowler studied about 4,700 people, followed from 1983 to 2003 as part of the Framingham Heart Study. (See “Dynamic spread of happiness in a large social network”; .pdf file here.) These subjects were embedded in a larger network of about 12,000 people; they had an average of 11 connections to others in the social network (including to friends, family, co-workers, and neighbors); and their happiness was assessed every few years using a standard measure.
The researchers found that social networks have clusters of happy and unhappy people within them that reach out to three degrees of separation. A person’s happiness is correlated with the happiness of their friends, their friends’ friends, and their friends’ friends’ friends. Happy people tended to be located in the center of their social networks and to be located in large clusters of other happy people. Each additional happy friend increased a person’s probability of being happy by about 9%. (For comparison, having an extra $5,000 in income — in 1984 dollars — is estimated to increase the probability of being happy by about 2%.)
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In an unpublished follow-up study, the researchers examined a group of about 1,700 college students on Facebook. They coded who appeared in photographs with whom. The average student had over 110 friends on Facebook, but they had an average of only six “picture friends” (i.e., people close enough that they tagged the student).
They then coded whether the students were smiling in their profile photographs, and mapped the network of students and their picture friends, making note of who was smiling and who was not.

The figure above is a map of part of this Facebook network in 2007. It contains about 350 students, each represented by a node; each line between two nodes indicates that the connected individuals were tagged in a photo together. Students who were smiling (and who were immediately surrounded by smiling people in their network) are colored yellow. Students who were frowning (and who are immediately surrounded by such serious looks) are colored blue. Shades of green indicate a mix of smiling and non-smiling friends.
The blue nodes and the yellow nodes strongly cluster together. Statistical analysis of the network shows that people who smile tend to have more friends (smiling is correlated with an average of one extra friend, which is significant, since the average person has only about 6 close friends). Those who smile are measurably more central to the network.
“Social Networks & Happiness“