A Majority-Vote Model On Multiplex Networks with Community Structure

TL;DR

This paper explores a majority-vote model on multiplex networks with community structure, analyzing how layer importance and community correlations influence opinion dynamics and steady states.

Contribution

It introduces a layer-preference parameter and studies its effects on opinion states, revealing new insights into community influence and phase transitions in multiplex networks.

Findings

Interlayer community correlation promotes polarized states.

Layer-preference affects phase diagrams of opinions.

Identifies three steady-state behaviors: mixed, consensus, polarized.

Abstract

We investigate a majority-vote model on two-layer multiplex networks with community structure. In our majority-vote model, the edges on each layer encode one type of social relationship and an individual changes their opinion based on the majority opinions of their neighbors in each layer. To capture the fact that different relationships often have different levels of importance, we introduce a layer-preference parameter, which determines the probability of a node to adopt an opinion when the node's neighborhoods on the two layers have different majority opinions. We construct our networks so that each node is a member of one community on each layer, and we consider situations in which nodes tend to have more connections with nodes from the same community than with nodes from different communities. We study the influence of the layer-preference parameter, the intralayer communities, and interlayer membership correlation on the steady-state behavior of our model using both direct numerical simulations and a mean-field approximation. We find three different types of steady-state behavior: a fully-mixed state, consensus states, and polarized states. We demonstrate that a stronger interlayer community correlation makes polarized steady states reachable for wider ranges of the other model parameters. We also show that different values of the layer-preference parameter result in qualitatively different phase diagrams for the mean opinions at steady states.