Limited cognitive adjustments in signed networks

Under the auspices of structural balance theory, the individuals in signed social networks will adjust their relations with their neighbours to reduce the stress induced by imbalanced triangles. In small networks individuals may be able to observe the impact of their adjustments upon the global balance of the network. But in larger networks this will not prove feasible, their local adjustments will only respond to their immediate neighbourhoods. Furthermore, adjustments may only centre upon the more important neighbours. We study whether limited cognition (i.e. variations in the number of important neighbours) affects the convergence of generated networks to balance. We find that limited cognition adjustment can drive the complete networks to global balance as long as the number of recognized neighbours exceeds an even number critical value. But under relaxed increase requirement, the complete network will go global balance only if the number (even number) of recognized neighbours exceeds a critical value. Critical values varies with network size, network density (d) and the initial ratio of positive links. But for incomplete network, less links among node will thwart the network converge to global balance. The sparser the incomplete network is and the lower ratio of initial positive edges, the harder for the network to converge to global balance. Some special imbalance substructures like the attractors can prevent the incomplete network to global balance. The experimental in a real email network also verify this results.