How might one test the hypothesis that graphs were sampled from the same distribution? Here, we compare two statistical tests that address this question. The first uses the observed subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the graph cumulants of the distribution. We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants.

中文翻译：

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用于网络比较的原则性（实用）测试

如何检验图形是从同一分布中采样的假设？在这里，我们比较了解决这个问题的两个统计测试。第一个使用观察到的子图密度本身作为基础分布的估计值。第二个测试使用一种新方法，将这些子图密度转换为分布图累积量的估计值。我们通过理论、模拟和实际数据的应用证明了使用图累积量的卓越统计能力。