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Stochastic Models for the Inference of Life Evolution

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

Ferretti, L., Mamino, M., Bianconi, G.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

2014

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.

Bibtex

@article{ferretti_condensation_2014,
Author = {Ferretti, Luca and Mamino, Marcello and Bianconi,
Ginestra},
Title = {Condensation and topological phase transitions in a
dynamical network model with rewiring of the links},
Journal = {Physical Review. E, Statistical, Nonlinear, and Soft
Matter Physics},
Volume = {89},
Number = {4},
Pages = {042810},
abstract = {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.},
doi = {10.1103/physreve.89.042810},
issn = {1550-2376},
language = {eng},
month = apr,
pmid = {24827296},
year = 2014
}

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