Signed networks capture the polarity of relationships between nodes, providing valuable insights into complex systems where both supportive and antagonistic interactions play a critical role in shaping the network dynamics. We propose a separable temporal generative framework based on multi-layer exponential random graph models, characterised by the assumption of conditional independence between the sign and interaction effects. This structure preserves the flexibly and explanatory power inherent in the binary network specification while adhering to consistent balance theory assumptions. Using a fully probabilistic Bayesian paradigm, we infer the doubly intractable posterior distribution of model parameters via an adaptive Metropolis-Hastings approximate exchange algorithm. We illustrate the interpretability of our model by analysing signed relations among U.S. Senators during Ronald Reagan's second term (1985-1989). Specifically, we aim to understand whether these relations are consistent and balanced or reflect patterns of supportive or antagonistic alliances.

翻译：符号网络能够捕捉节点间关系的极性，为复杂系统提供重要洞见，其中支持性与对抗性交互在塑造网络动态过程中均发挥着关键作用。我们提出一种基于多层指数随机图模型的可分离时序生成框架，其核心特征在于假设符号效应与交互效应之间具有条件独立性。该结构在保持二元网络设定固有灵活性与解释力的同时，遵循一致性平衡理论假设。通过完全概率化的贝叶斯范式，我们采用自适应Metropolis-Hastings近似交换算法推断模型参数的双重难解后验分布。通过分析罗纳德·里根第二任期（1985-1989年）期间美国参议员间的符号关系，我们阐释了该模型的可解释性。具体而言，本研究旨在探究这些关系是保持稳定平衡，还是反映了支持性或对抗性联盟的模式。