Recently, there has been some talk about how major social networks are not as cool or useful anymore. Most of these arguments focus on the angle that the dominant networks are too large and broad, making it hard to create a more intimate environment for their users.
In a recent paper with Ganesh Iyer, we study this question from a different angle. We focus on the incentive of users to contribute to the conversation. Importantly, people want to be heard, thus they only make an effort to send out messages if they can expect to be listened to. The main result of the paper demonstrates that as the network becomes denser and as each user competes with more of their peers for the attention of listeners, it takes more effort to remain relevant. This, in turn may deter users from contributing as reflected in what's called participation inequality. That is, that only a few percentage of users actively contribute.
Having links in a social network is nonetheless very important as provides reach to users who decide to contribute, but after a threshold too many links deter contributors. Perhaps this is the reason for some new players limiting the number of connections that a user can have.
The figure shows the number of users who would decide to contribute as a function of network density in a small network (for different levels of contribution cost/difficulty). As density increases, initially more people contribute, but after a threshold the number of contributing users declines: