Network structures and agreement in social network simulations

Networks are very evident in the physical world and particularly in social structures. One focus of research is on investigating the development and maintenance of social network structures. Social networks may be typically categorised as random, scale-free or hierarchical structures. A key research question is how the structure and parameters of a network affect the stability of opinion within the network. In a previous study, we examined the case for random network structures. In this work, we show how complex systems models can be used to investigate the effects of various parameters (including the number of layers and the number of links per node) in hierarchical and scale-free network structures. The models are used to investigate whether the network reaches a stable collective state, where the opinions of individuals remain constant, or an unstable state, where the opinions of individuals continue to change. Several important results emerge. One is that flat hierarchies, which possess few layers and many links per node, are more likely to be unstable than deeper hierarchies. Another is that regardless of the network topology, the number individuals whose opinion continues to change settles to a relatively stable level. We also demonstrate the inherent stability of scale-free networks. This work has implications for how network structures should be organized, in order to exploit stability or dynamic behaviour, in particular for political, organisational, social and educational contexts.