Many two-sample network hypothesis testing methodologies operate under the implicit assumption that the vertex correspondence across networks is a priori known. In this paper, we consider the degradation of power in two-sample graph hypothesis testing when there are misaligned/label-shuffled vertices across networks. In the context of random dot product and stochastic block model networks, we theoretically explore the power loss due to shuffling for a pair of hypothesis tests based on Frobenius norm differences between estimated edge probability matrices or between adjacency matrices. The loss in testing power is further reinforced by numerous simulations and experiments, both in the stochastic block model and in the random dot product graph model, where we compare the power loss across multiple recently proposed tests in the literature. Lastly, we demonstrate the impact that shuffling can have in real-data testing in a pair of examples from neuroscience and from social network analysis.

翻译：许多双样本网络假设检验方法隐含假设网络间的顶点对应关系是先验已知的。本文研究了当网络间存在顶点错配/标签混洗时，双样本图假设检验效能的退化现象。在随机点积图和随机分块网络模型框架下，我们理论探索了基于估计边概率矩阵或邻接矩阵间Frobenius范数差异的一对假设检验因混洗导致的效能损失。通过随机分块模型与随机点积图模型中的大量模拟实验，进一步验证了检验效能的损失，并与文献中近期提出的多种检验方法进行了效能损失对比。最后，我们通过神经科学和社会网络分析中的两个实例，展示了混洗对真实数据检验的实际影响。