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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.<\/jats:p>","DOI":"10.1093\/biomet\/asad080","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T18:51:57Z","timestamp":1703184717000},"page":"743-754","source":"Crossref","is-referenced-by-count":6,"title":["Central limit theorems for local network statistics"],"prefix":"10.1093","volume":"111","author":[{"given":"P A","family":"Maugis","sequence":"first","affiliation":[{"name":"Department of Statistical Science, University College London , Gower Street , London WC1E 6BT, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,12,22]]},"reference":[{"key":"2024090418514543600_asad080-B1","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/s10115-016-0965-5","article-title":"Graphlet decomposition: framework, algorithms, and applications","volume":"50","author":"Ahmed","year":"2017","journal-title":"Knowl. 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