Instability of social network dynamics with stubborn links

Abstract: This paper studies the signed networks in the presence of stubborn links, based on the structural balance theory. Each agent in the network has a mixture of positive and negative links represent friendly and antagonistic interactions and his stubbornness about interactions. Structural balance theory affirms that in signed social networks with simultaneous friendly/hostile interactions, there is a general tendency of evolving over time to reduce the tensions. From this perspective, individuals iteratively invert their own sentiments to reduce the felt tensions induced by imbalance. In this paper, we investigate the consequences of the agents' stubbornness on their interactions. We define stubbornness as an extreme antagonistic interaction which is resistant to change. In the current paper, we investigated if the presence of stubborn links renders an impact on the balance state of the network and whether or not the degree of balance in a signed network depends on the location of stubborn links. Our results show that a poorly balanced configuration consists of multiple antagonistic groups. Both analytical and simulation results demonstrate that the global level of balance of the network is more influenced by the locations of stubborn links in the resulting network topology than by the fraction of stubborn links. This means that even with a large fraction of stubborn links the network would evolve towards a balanced state. On the other hand, if a small fraction of stubborn links are clustered in five stubborn communities, the network evolves to an unbalanced state.