Condensation and topological phase transitions in a dynamical network model with rewiring of the links

摘要

Growing network models with both heterogeneity of the nodes and topologicalconstraints can give rise to a rich phase structure. We present a simple modelbased on preferential attachment with rewiring of the links. Rewiringprobabilities are modulated by the negative fitness of the nodes and by theconstraint for the network to be a simple graph. At low temperatures and highrewiring rates, this constraint induces a Bose-Einstein condensation of pathsof length 2, i.e. a new phase transition with an extended condensate of links.The phase space of the model includes further transitions in the scaling of theconnected component and the degeneracy of the network.