结构平衡理论和地位理论是社交网络领域的重要理论，可以用来分析同时具有正向和负向连边的社交符号网络。提出了3种新的随机断边重连零模型，基于随机断边重连和符号随机置乱两大类零模型，对符号社交网络的地位理论和结构平衡理论进行了系统研究。发现基于零模型不但可以验证两种理论在实证网络中的准确性，还能揭示正边、负边拓扑结构和连边符号相关性对于整个网络性质的影响。提出了一个新框架，研究能否将有向符号网络转化为无向符号网络，发现目前常用的将有向符号网络转化成无向符号网络的方法在有些情况下对于研究社交网络理论是不合适的，存在着信息损失；讨论了非符号有向网络中的势能理论。
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.
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