We propose new mathematical programming models for optimal partitioning of a signed graph into cohesive groups. To demonstrate the approach's utility, we apply it to identify coalitions in US Congress since 1979 and examine the impact of polarized coalitions on the effectiveness of passing bills. Our models produce a globally optimal solution to the NP-hard problem of minimizing the total number of intra-group negative and inter-group positive edges. We tackle the intensive computations of dense signed networks by providing upper and lower bounds, then solving an optimization model which closes the gap between the two bounds and returns the optimal partitioning of vertices. Our substantive findings suggest that the dominance of an ideologically homogeneous coalition (i.e. partisan polarization) can be a protective factor that enhances legislative effectiveness.

中文翻译：

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通过对签署的政治合作网络进行最佳划分来检测联盟

我们提出了新的数学规划模型，用于将有符号图最佳划分为内聚组。为了证明该方法的效用，我们将其应用于确定自 1979 年以来美国国会中的联盟，并检查两极分化的联盟对通过法案有效性的影响。我们的模型为最小化组内负边和组间正边的总数的 NP 难问题生成了全局最优解。我们通过提供上界和下界来解决密集有符号网络的密集计算，然后求解一个优化模型，该模型缩小两个边界之间的差距并返回顶点的最佳分区。我们的实质性研究结果表明，意识形态上同质的联盟（即