Dynamics of opinion forming in structurally balanced social networks

The aim of this paper is to shed light on how the social relationships between individuals influence their opinions in the case of structurally balanced social networks. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends. A classical example of this situation is a two-party political system. The paper studies the process of opinion forming on such a social community, starting from the observation that the property of structural balance is formally analogous to the monotonicity property of dynamical systems. The paper shows that under the assumption that individuals are positively influenced by their friends and negatively influenced by their enemies, monotone dynamical systems, due to their order-preserving solutions, are natural candidates to describe the highly predictable process of opinion forming on structurally balanced networks.