Complex networks

Complex networks with preferential attachment and node features

• • Nodes in a network are sometimes homogeneous, but they often have different features: spatial position, quality or fitness, functional modules (e.g. in genetic networks) etc. We studied how the presence of spatial constraints [4] or more general features of the nodes [3] affects the properties of scale-free networks generated by preferential attachment mechanisms. We showed that the degree distribution of these models is scale-free and robust and that these models present a complex pattern of assortativity. We also proved that some models with preferential attachment on the sphere are dual to static networks on hyperbolic spaces [2]. More complex models with negative fitness, rewiring and topological constraints result in new phase transitions with condensation of paths and a complex phase space [1]. We also studied the dynamics of condensation and the turnover of condensate nodes in the fitness models [5].

    1. Ferretti L*, Mamino M*, Bianconi G, Condensation and topological phase transitions in a dynamical network model with rewiring of the links, Phys. Rev E 89 042810 (2014). arXiv.

    2. Ferretti L, Cortelezzi M, Mamino M, Duality between preferential attachment and hyperbolic networks, Eur. Phys. Lett. 105 38001 (2014). arXiv.

    3. Ferretti L*, Cortelezzi M*, Bin Y, Marmorini G and Bianconi G, Features and heterogeneities in growing network models, Phys. Rev. E 85, 066110 (2012). arXiv.

    4. Ferretti L and Cortelezzi M, Preferential attachment in growing spatial networks, Phys. Rev. E. 84,016103 (2011). arXiv.

    5. Ferretti L and Bianconi G, Dynamics of condensation in growing complex networks, Phys. Rev. E 78,056102 (2008). arXiv.

Dynamics on complex networks

• • We analyzed the dynamics of a phase transition on complex networks.

    1. Halu A, Ferretti L, Vezzani A and Bianconi G, Phase diagram of the Bose-Hubbard Model on Complex Networks, Eur. Phys. Lett. 99 18001 (2012). arXiv.