Irreducibility of multilayer network dynamics: the case of the voter model
Abstract
We address the issue of the reducibility of the dynamics on a multilayer network to an equivalent process on an aggregated singlelayer network. As a typical example of models for opinion formation in social networks, we implement the voter model on a twolayer multiplex network, and we study its dynamics as a function of two control parameters, namely the fraction of edges simultaneously existing in both layers of the network (edge overlap), and the fraction of nodes participating in both layers (interlayer connectivity or degree of multiplexity). We compute the asymptotic value of the number of active links (interface density) in the thermodynamic limit, and the time to reach an absorbing state for finite systems, and we compare the numerical results with the analytical predictions on equivalent singlelayer networks obtained through various possible aggregation procedures. We find a large region of parameters where the interface density of large multiplexes gives systematic deviations from that of the aggregates. We show that neither of the standard unweighted aggregation procedures is able to capture the highly nonlinear increase in the lifetime of a finite size multiplex at small interlayer connectivity. These results indicate that multiplexity should be appropriately taken into account when studying voter model dynamics, and that, in general, singlelayer approximations might be not accurate enough to properly understand processes occurring on multiplex networks, since they might flatten out relevant dynamical details.
 Publication:

New Journal of Physics
 Pub Date:
 February 2016
 DOI:
 10.1088/13672630/18/2/023010
 arXiv:
 arXiv:1507.08940
 Bibcode:
 2016NJPh...18b3010D
 Keywords:

 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Social and Information Networks;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 10 pages, 6 figures