The structural balance and the status are important issues in social network fields, which can be used to analyze signed social networks with a mixture of positive and negative interactions. In this study firstly three novel random link-mixing null models are proposed. Then the status and structural balance theories of signed social networks are studied based on the random link-mixing null models as well as the random sign-mixing null models. It is shown that, based on null models, not only the accuracy obtained based on both theories can be verified in the study of empirical networks, but also the impacts of the positive and negative edge topologies and the edge signed correlation on the whole network properties can be revealed. Finally, a new framework is proposed to study whether the directed signed networks can be transformed into the undirected signed networks. It is confirmed that the common methods for transforming the directed signed networks into the undirected signed networks are not suitable for studying social network theories, and the potential theory in unsigned directed networks is also studied.

signed network  /  null model  /  online social networks  /  network motif