In social networks comprised of positive (P) and negative (N) symmetric relations, individuals (nodes) will, under the stress of structural balance, alter their relations (links or edges) with their neighbours, either from positive to negative or vice versa. In the real world, individuals can only observe the influence of their adjustments upon the local balance of the network and take this into account when adjusting their relationships. Sometime, their local adjustments may only respond to their immediate neighbourhoods, or centre upon the most important neighbour. To study whether limited memory affects the convergence of signed social networks, we introduce a signed social network model, propose random and minimum memory-based sign adjustment rules, and analyze and compare the impacts of an initial ratio of positive links, rewire probability, network size, neighbor number, and randomness upon structural balance under these rules. The results show that, with an increase of the rewiring probability of the generated network and neighbour number, it is more likely for the networks to globally balance under the minimum memory-based adjustment. While the Newmann-Watts small world model (NW) network becomes dense, the counter-intuitive phenomena emerges that the network will be driven to a global balance, even under the minimum memory-based local sign adjustment, no matter the network size and initial ratio of positive links. This can help to manage and control huge networks with imited resources.
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