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：许多双模网络假设测试方法在以下隐含假设下运作:跨网络的顶端通信是先验已知的。在本文中,当跨网络的双模图形假设测试出现错配/标签擦拭的脊椎时,我们考虑的是跨网络的双模图假设测试中的力量退化。在随机点产品和随机随机切换区块模型网络中,我们理论上探索了根据Frobenius标准差分对估计边缘概率矩阵或相邻矩阵进行一对假设测试而进行重排测试造成的能量损失。测试能力的损失通过许多模拟和实验得到进一步的加强,这些模拟和实验既在随机区块模型中,又在随机点图产品图模型中,我们比较文献中最近提出的多项测试的功率损失。最后,我们展示了在神经科学和社会网络分析的一对一对一示例中进行真实数据测试时,摇动对实际数据测试可能产生的影响。</s>