Clusters and the entropy in opinion dynamics on complex networks

TL;DR

This paper explores how opinion clusters form in complex networks using a modified Hegselmann-Krause model, revealing optimal parameters for cluster diversity and the influence of network structure on opinion dynamics.

Contribution

It introduces Shannon entropy to quantify opinion clusters and analyzes the effects of network topology and parameters on cluster formation and diversity.

Findings

Optimal stubbornness maximizes cluster number and entropy.

Optimal bounded confidence minimizes cluster number and entropy.

Network structure influences cluster profiles and consensus formation.

Abstract

In this work, we investigate a heterogeneous population in the modified Hegselmann-Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network structures affect cluster profiles indeed. A large average degree favors consensus for making different networks more similar with complete graphs. The network size has limited impact on cluster profiles of heterogeneous populations on scale-free networks but has significant effects upon those on small-world networks.