So does happiness spread the same way through online social networks? Maybe. One study showed that someone who's smiling in their profile picture is more likely to have friends who smile in their profile pictures as well. Another study showed that people who were smiling in their picture had an average of one more friend than Facebook users who weren't smiling.
This research seems to follow the Christakis-Fowler study findings about how happiness clusters. People tend to cluster in happy groups. The people toward the center of that group are more likely to be happy than the people on the periphery. The same was verified in the Facebook study. People at the center of a social circle had more friends, and more smiling friends, in their networks than people on the edges of social webs. On the outskirts of the circle, even if the person is smiling in their profile picture, he or she is more likely to have friends who aren't and will have less friends overall.
To understand how it's possible for happiness to spread through a social network, it's important to understand how happiness spreads anywhere. There are three basic ways that happiness moves through a group of people:
Confounding is the term used to describe what happens when a group of people who are loosely connected share similar life experiences. An example of this would be a group of people who work in the same office or live in the same neighborhood. Positive experiences affect them individually and as a whole, as do negative experiences. This is one way people living in the same area may experience a cluster of happiness.
Homophily is when happy people choose each other as friends. Drawn together like magnets, happy people find others that share their life view and become friends.
Induction is the sensation of happiness in one person leading to happiness in others, through emotional contagion. Happiness is spread through who we choose as friends, shared life experiences, and hanging out with people who are emotionally wired for happiness. Can this translate to an online community? There is no firm answer, but there doesn't seem to be a reason why it wouldn't.