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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.

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