Opinion formation on multiplex scale-free networks

¹ School of Electrical and Electronic Engineering, Nanyang Technological University - Singapore 639798, Singapore
² Complexity Institute, Nanyang Technological University - 18 Nanyang Drive, Singapore 637723, Singapore
³ Department of Mathematics, Shanghai University - Shanghai, China
⁴ Center for Brain Inspired Computing Research, Department of Precision Instrument, Tsinghua University Beijing, China
⁵ Center for OPTical IMagery Analysis and Learning (OPTIMAL) and School of Mechanical Engineering Northwestern Polytechnical University - Xi'an, 710072, China

^(a) egxxiao@ntu.edu.sg
^(b) zhenwang0@gmail.com

Received: 11 December 2017
Accepted: 28 February 2018

Abstract

Most individuals, if not all, live in various social networks. The formation of opinion systems is an outcome of social interactions and information propagation occurring in such networks. We study the opinion formation with a new rule of pairwise interactions in the novel version of the well-known Deffuant model on multiplex networks composed of two layers, each of which is a scale-free network. It is found that in a duplex network composed of two identical layers, the presence of the multiplexity helps either diminish or enhance opinion diversity depending on the relative magnitudes of tolerance ranges characterizing the degree of openness/tolerance on both layers: there is a steady separation between different regions of tolerance range values on two network layers where multiplexity plays two different roles, respectively. Additionally, the two critical tolerance ranges follow a one-sum rule; that is, each of the layers reaches a complete consensus only if the sum of the tolerance ranges on the two layers is greater than a constant approximately equaling 1, the double of the critical bound on a corresponding isolated network. A further investigation of the coupling between constituent layers quantified by a link overlap parameter reveals that as the layers are loosely coupled, the two opinion systems co-evolve independently, but when the inter-layer coupling is sufficiently strong, a monotonic behavior is observed: an increase in the tolerance range of a layer causes a decline in the opinion diversity on the other layer regardless of the magnitudes of tolerance ranges associated with the layers in question.