You have five friends who ski. Three are on the ski team. You think about joining, but ultimately decide against it. But then the other two join, and soon so do you.
This illustrates the first law of social network growth: The probability p of joining an online community is a function of the number of friends k already in that community.
What's more interesting is this. If your friends are also friends, you're significantly more likely to join. Almost 2.5 times more likely. That's huge.
Social networking theory has this concept of triads. Let's say there are three people, A-B-C. Person B is friends with person A. Person B is also friends with person C. If person A knows person C, the triad is closed. If person A does not know person C, the triad is open.
So we know that having more friends in a group makes you more likely to join. And if your friends all know each other, your chances of joining go up even further.
The paradox is this: The higher the ratio of closed triads a group has, the slower it grows.
If each individual is more likely to join the group, how can the group as a whole grow more slowly? It seems impossible.
One possible explanation is that tightly connected groups become cliqueish. Indeed, there is some evidence that groups based around common bonds between users are harder to join than groups based around a common identity. However, if cliqueishness really were the reason these groups grew more slowly then why are individuals so much more likely to join groups with many closed triads? This theory seems questionable.
Another possible explanation is that when the network is growing very fast, the nodes don't have enough time to connect. When the rate of growth slows down, the nodes then play catch-up and connect along the edges. This theory also does not feel entirely satisfactory. Social networks go to great lengths to reward those with many friends, and users go out of their way to add anyone they can think of.
While more research is needed, the preliminary results already raise valuable questions:
Why should the fact that your friends in a community know each other make you more likely to join?
Does large density of closed triads represent cliquishness?
What are the structural features that influence whether a given individual will join a particular group?
What are the structural features that influence whether a given group will grow significantly?
The answers are still up for debate. There's still so much we don't know. But in some ways, just having the questions will give future designers an enormous advantage.
Backstrom, L., Huttenlocher, D., Kleinberg, J., & Lan, X. (In press). Group formation in large social networks: membership, growth, and evolution. [PDF]