Social network evolution based on agent centrality

We consider a general stochastic model of social network formation and evolution. In this model, agents form and sever links basing their decisions on the centrality of their potential partners. We consider different types of centrality measures and show that they can be unified in our model. We show how the emergence of hierarchies depends on the volatility of the environment and that there exists a sharp transition from strongly centralized to decentralized networks. Finally, we solve the time evolution of the model and show that the stationary networks exhibit topological properties that qualitatively match with features of social and economic networks.