Opinion Polarization Over Signed Social Networks With Quasi-Structural Balance

Abstract

In social networks with mixed trust and distrust relationships, polarization is a common class of opinion evolutionary phenomena. Existing studies have generally believed that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">structural balance</i> on networks is a crucial condition for the emergence of opinion polarization under DeGroot-style interactions. Unlike existing studies, this article aims to establish a new updating model based on DeGroot-style interactions, thereby relaxing the network structure requirement of achieving opinion polarization to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quasi-structural balance</i> , which is a more general concept and can include structural balance as a special case. With the assistance of the method of products convergence of infinite super-stochastic matrices, a comprehensive analysis of the model is carried out, and algebraic conditions on the degrees of trust and distrust among agents are established, so as to ensure the realization of opinion polarization on quasi-structurally balanced networks. At last, numerical simulations are provided to verify the theoretical results.