AI 中文总结
针对稀疏随机图的中心节点邻域度开发诊断统计量，转化为拟合优度检验，经模拟及高中接触、arXiv合著等网络验证，可区分模型误设与残留邻域趋势。
AI 中文摘要
具有几乎相同度分布的网络，其中心节点可位于截然不同的邻域中。我们基于度为k的顶点的邻居平均度开发了一种模型诊断方法。在秩一非均匀随机图下，该统计量具有度不变的中心和k^(-1/2)的波动；在非秩一核下，关于根类型的后验不确定性可同时决定中心和尺度；在线性优先连接下，该统计量随(m+δ)logk增长。我们将这些模型特定的极限转化为针对指定稀疏图原假设的拟合优度检验，以及用于残留中心邻域趋势的加权对数度斜率检验。模拟评估了原假设校准、度分布误设以及对度匹配优先连接替代的功效。在高中接触网络和arXiv合著网络上的应用表明，该方法可区分水平误设与异配及正残留趋势，Reddit交互网络提供了进一步的附录示例。
英文摘要
Networks with nearly identical degree distributions can place their hubs in sharply different neighborhoods. We develop a model diagnostic based on the mean degree of the neighbors of a degree-$k$ vertex. Under rank-one inhomogeneous random graphs, this statistic has degree-invariant centering and $k^{-1/2}$ fluctuations. Under non-rank-one kernels, posterior uncertainty about the root type can instead determine both centering and scale. Under linear preferential attachment, the statistic grows as $(m+δ)\log k$. We turn these model-specific limits into goodness-of-fit tests for specified sparse-graph nulls and a weighted log-degree slope test for residual hub-neighborhood trends. Simulations evaluate null calibration, degree-distribution misspecification, and power against degree-matched preferential-attachment alternatives. Applications to high-school contact and arXiv coauthorship networks show that the method separates level misspecification from disassortative and positive residual trends. Reddit interaction networks provide a further appendix example.
