Non-consensus opinion model on directed networks

TL;DR

This paper investigates how the structure of directed networks influences the coexistence and dominance of opinions, revealing that increased directionality and degree correlation favor the majority opinion.

Contribution

It introduces a non-consensus opinion model on directed networks and explores how network directionality and degree correlation affect opinion dynamics.

Findings

Higher directionality $\xi$ strengthens majority opinion dominance.

Increased degree correlation $ ho$ reduces minority opinion survival.

Directed network structure significantly impacts opinion competition outcomes.

Abstract

Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a non-consensus opinion model introduced by Shao et al. \cite{shao2009dynamic} on directed networks. We define directionality $\xi$ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient $\rho$ between the indegree and outdegree of a node to quantify the relation between the indegree and outdegree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality $\xi$ and linear correlation coefficient $\rho$ and to study how $\xi$ and $\rho$ impact opinion competitions. We find that, as the directionality $\xi$ or the indegree and outdegree correlation $\rho$ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered.