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Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities are modulated by the negative fitness of the nodes and by the constraint for the network to be a simple graph. At low temperatures and high rewiring rates, this constraint induces a Bose-Einstein condensation of paths of 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 size of the connected component and the degeneracy of the network.

Original publication

DOI

10.1103/physreve.89.042810

Type

Journal article

Journal

Physical review. E, Statistical, nonlinear, and soft matter physics

Publication Date

04/2014

Volume

89

Addresses

Systématique, Adaptation, et Evolution (UMR 7138), UPMC Université de Paris 06, CNRS, MNHN, IRD, Paris, France and CIRB, Collège de France, Paris, France.