Irreducibility of multilayer network dynamics: the case of the voter model

TL;DR

This paper investigates whether the dynamics of the voter model on multilayer networks can be accurately represented by single-layer network aggregations, revealing significant deviations and nonlinear effects that challenge common simplifications.

Contribution

It demonstrates that standard aggregation methods often fail to capture the nonlinear dynamics of voter models on multiplex networks, emphasizing the importance of considering multiplexity.

Findings

Significant deviations in interface density between multiplexes and aggregated networks.

Standard aggregation procedures do not capture nonlinear increases in system lifetime.

Multiplexity critically influences voter model dynamics, affecting predictions.

Abstract

We address the issue of the reducibility of the dynamics on a multilayer network to an equivalent process on an aggregated single-layer network. As a typical example of models for opinion formation in social networks, we implement the voter model on a two-layer 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 single-layer 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 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, single-layer approximations might be not accurate enough to properly understand processes occurring on multiplex networks, since they might flatten out relevant dynamical details.