发表机构
Université Laval（拉瓦尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析了网络依赖性度量Moran's $I$和同配性的渐近零分布，发现网络拓扑决定收敛速率和极限分布，且同配性在强异质稠密网络中可能失效。
AI 中文摘要
本研究探讨了在零假设下（即高斯节点属性$Y$与网络结构独立），网络上定义的两种依赖性度量——Moran's $I$统计量和Newman同配性——的渐近行为。我们证明，随着网络规模的增大，网络结构直接影响这些度量收敛到正态分布的速率。我们进一步证明，在某些情况下，这些依赖性度量在零假设下的均值在渐近意义上仍不可忽略，因此在计算检验统计量时必须明确考虑这些均值。对多种模拟网络和真实网络的应用也表明，只有当网络不是强异质时，正态近似才表现良好。网络拓扑结构决定了收敛到正态分布的速率以及极限分布是否为高斯分布。在度异质性不消失的稠密网络中，我们进一步证明，即使Moran's $I$表现良好，同配性也可能无法作为有效的检验统计量，而一个主导节点会使两者都失效。
英文摘要
This study investigates the asymptotic behavior of two dependence measures defined on networks, Moran's $I$ statistic and Newman's assortativity, under the null hypothesis that a Gaussian node attribute $Y$ is independent of the network structure. We demonstrate that the structure of the network directly affects the convergence rate to normality of these measures as the size of the network increases. We further establish that, in some instances, the mean values of these dependence measures under the null hypothesis remain non-negligible asymptotically and must therefore be explicitly accounted for when calculating the test statistics. Applications to a variety of simulated and real networks also reveal that the normal approximation performs well only when the network is not strongly heterogeneous. Network topology determines both the convergence rate to normality and whether the limiting distribution is Gaussian. In dense networks whose degree heterogeneity does not vanish, we further show that assortativity can fail to be a valid test statistic even though Moran's $I$ remains well behaved, whereas a dominating node invalidates both.
CommentsThis is a preprint submitted for review at the Journal of Complex Networks and has not yet been peer-reviewed in its current form
