AI 中文总结
该研究针对由图函子定义的Erdős–Rényi图，提出基于子图计数的拟合优度检验，经图泛函分解揭示抵消效应，得到对所有对立假设一致的检验，有限规模表现通过模拟验证。
AI 中文摘要
齐次随机图，又称Erdős–Rényi图，是稠密随机图族的子集，由图函子（graphon）定义。我们分析了若干基于子图计数的该类模型拟合优度检验，为获取检验统计量的极限原分布，我们采用图泛函分解，该分解揭示了一种抵消效应。受拟随机性（quasirandomness）结论启发，我们得到了对所有对立假设均一致的检验，并用两类流行的参数子族评估其他检验。理论结果针对图规模n→∞的极限情况，有限n的表现通过模拟示例说明。
英文摘要
Homogeneous random graphs, also known as Erd{\H os}-Rényi graphs, are a subset of the family of dense random graphs, specified by a graphon. We analyze several goodness-of-fit tests for these models that are based on subgraph counts. To obtain the limiting null distribution of the test statistics we use a decomposition of graph functionals, which reveals a cancellation effect. Motivated by a quasirandomness result we obtain a test that is consistent against all alternatives, and we use two popular parametric subfamilies to evaluate the other tests. The theoretical results refer to the limit $n\to \infty$ of the size $n$ of the graph, the behavior for finite $n$ is illustrated by simulations.
