Opinion Dynamics Considering Matthew Effect Under Switching Topology in Social Networks

Abstract

Matthew effect refers to a phenomenon where the rich get richer and the poor get poorer. In this paper, a Matthew effect under switching topology (MUST) model is proposed to describe the evolution of the opinion dynamics in social networks. On social media, there may be numerous different opinions on a same social event, and initially, people will tend to believe the dominant opinion. However, when new evidence related to the event arises, the dominant opinion may be changed. In order to investigate the Matthew effect on public opinion, a feedback mechanism based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -winners-take-all ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -WTA) operation is leveraged to analyze and describe the polarization phenomenon in the evolution of opinions, which involves a competition between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> participants with only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> winners, with the others defined as losers. Further, a non-negative weighted graph with switching topology is constructed to describe changing connections between opinions in a social network. In addition, convergence and stability analysis on the proposed MUST model is provided. Finally, the experimental results visually indicate the validity and feasibility of the proposed MUST model.