Threshold q-voter model with signed relationships

Abstract

Many real social networks, especially online social networks, intrinsically involve negative links as well as positive ones, which describe a social phenomenon where humans label each other as friends or foes. The positive link and the negative link carry the opposite effect on the dynamics occurring in social networks. In the paper, we extend the threshold q-voter model to a fully connected signed network and analyze the collective phenomenon of opinion formation by employing the backward Fokker–Planck formalism. We find that the mixture of positive and negative relationships, just as the noise parameter ϵ, plays an important role in the phase transition of opinion formation. Randomness and anti-conformity relationships hamper the emergence of the majority states in opinion formation, while the threshold value q 0 plays a vital role in the robustness of a system under the noise effect and the signs competition. Numerical simulation results confirm our theoretical analysis and demonstrate the effect of signed relationships on the diversity in society.