Nonlinear growth and condensation in multiplex networks.
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of nonlinear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of nonlinearity these models allow us to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which one node in each layer attracts an extensive fraction of all the edges.
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom.
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Nicosia
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom.
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Bianconi
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom.
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Latora
Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France.
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Barthelemy