Cost of Collaboration vs Individual Effort in Social Networks

We study the dynamics of social networks in terms of population growth and control of user behavior. Most of the current research in social networks focus on static analysis through graph theoretic models to represent the networks or focus on modeling the traffic. Here, we study the cost of collaborative vs individualistic behavior of users in order to grow their network size in a social network. Each user incurs a cost (monetary or emotional) for collaboration. We formulate the behavior of the users as a non-linear optimization problem with a cost. The objective function of the optimization problem is obtained using a stochastic analysis of population growth in social networks, based on the first-passage time of a birth-death process. The stochastic model is validated by comparison with real data obtained from Twitter Results indicate that a homogeneous social network (in which users have similar characteristics) will be individualistic. However, heterogeneous social networks (users with different characteristics) exhibit a threshold effect, i.e., there is a minimum cost, below which the network is as collaborative as desired and a maximum cost above which the network is individualistic as required. To the best of our knowledge, this is one of the first analysis of dynamics of user behavior and temporal population growth in social networks.