On the role of volatility in the evolution of social networks
  We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition between order -- promoted by the efforts of agents to coordinate -- and disorder induced by volatility in the underlying social network. We find that when volatility affects mostly the decay of links, the model exhibit a sharp transition between an ordered phase with a dense network and a disordered phase with a sparse network. When volatility is mostly node-based, instead, only the symmetric (disordered) phase exists These two regimes are separated by a second order phase transition of unusual type, characterized by an order parameter critical exponent $\beta=0^+$. We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction. 
Daniele De Martino and Matteo Marsili