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In this paper, we investigate the influence of the dipolar magnetic interaction on the current-driven vortex dynamics in a two-dimensional array of nanodisks. A general formula is established for the prediction of the correlation between the restoring force of the target nanodisk and the polarities and circulations of the neighboring vortices. Large numbers of possible magnetization configuration combinations among the target and the surrounding neighbors are reduced into four groups under an extreme condition. The maximum and minimum restoring forces are analytically derived, which can be used to predict the critical switching current dependence on the magnetic configuration combinations of vortices.