Leader-Driven Opinion Dynamics in Signed Social Networks With Asynchronous Trust/Distrust Level Evolution

TL;DR

This paper investigates how a leader influences opinion formation in signed social networks with asynchronous trust/distrust updates, establishing conditions for consensus and polarization through theoretical analysis and simulations.

Contribution

It introduces a novel asynchronous trust/distrust evolution model based on opinion differences and analyzes its impact on opinion dynamics in signed networks.

Findings

Conditions for opinion consensus and polarization are derived.

The model's predictions are validated through simulations on real networks.

Abstract

Trust and distrust are common in the opinion interactions among agents in social networks, and they are described by the edges with positive and negative weights in the signed digraph, respectively. It has been shown in social psychology that although the opinions of most agents (followers) tend to prevail, sometimes one agent (leader) with a firm stand and strong influence can impact or even overthrow the preferences of followers. This paper aims to analyze how the leader influences the formation of followers' opinions in signed social networks. In addition, this paper considers an asynchronous evolution mechanism of trust/distrust level based on opinion difference, in which the trust/distrust level between neighboring agents is portrayed as a nonlinear weight function of their opinion difference, and each agent interacts with the neighbors to update the trust/distrust level and opinion at the times determined by its own will. Based on the related properties of sub-stochastic and super-stochastic matrices, the inequality conditions about positive and negative weights to achieve opinion consensus and polarization are established. Some numerical simulations based on two well-known networks called the ``12 Angry Men" network and the Karate Club network are provided to verify the correctness of the theoretical results.