Central limit theorems for local network statistics

• 成果类型: Article
• 署名作者: Maugis, P. A.
• 署名单位: University of London; University College London
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad080
• 发表日期: 2024
• 页码: 743754
• 关键词: U-STATISTICS; subgraph counts; models; approximation; distributions; Consistency; graphs

摘要

Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making existing approaches unable to describe vertex-specific characteristics. In contrast, rooted subgraphs focus on vertex neighbourhoods, and are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model that generalizes most statistical network models. This result enables a shift in the statistical analysis of 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 gender and race are significant predictors of local friendship patterns.