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We develop a dynamic network formation model that can explain the observed nestedness in real-world networks. Links are formed on the basis of agents' centrality and have an exponentially distributed life time. We use stochastic stability to identify the networks to which the network formation process converges and find that they are nested split graphs. We completely determine the topological properties of the stochastically stable networks and show that they match features exhibited by real-world networks. Using four different network datasets, we empirically test our model and show that it fits well the observed networks.