论文标题
本地网络统计的中心限制定理
Central limit theorems for local network statistics
论文作者
论文摘要
子图计数 - 特别是三角形等小形状的发生数量 - 表征了随机网络的属性，因此已将广泛用作用作网络摘要统计信息。但是，子图通常在全球范围内进行计数，现有方法无法描述顶点特定的特征。另一方面，扎根子图计数 - 重点关注任何给定顶点的社区的计数 - 是本地网络属性的基本描述。我们在不均匀的随机图中得出了根部子图计数的渐近关节分布，该模型概括了许多流行的统计网络模型。该结果使大图的统计分析从估计网络摘要到估算链接本地网络结构和顶点特异性协变量的模型的统计分析。例如，我们考虑一个学校的友谊网络，并表明当地的友谊模式是性别和种族的重要预测指标。
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically counted globally, and existing approaches fail to describe vertex-specific characteristics. On the other hand, rooted subgraph counts - counts focusing on any given vertex's neighborhood - are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model which generalizes many popular statistical network models. This result enables a shift in the statistical analysis of large graphs, from estimating network summaries, to estimating models linking local network structure and vertex-specific covariates. As an example, we consider a school friendship network and show that local friendship patterns are significant predictors of gender and race.
