{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-note-on-estimating-global-subgraph-counts","title":"A note on estimating global subgraph counts by sampling","arxiv_id":"2210.11336","date":"2022-10-20","proceeding":null,"authors":["Svante Janson","Valentas Kurauskas"],"abstract":"We give a simple proof of a generalization of an inequality for homomorphism counts by Sidorenko (1994). A special case of our inequality says that if $d_v$ denotes the degree of a vertex $v$ in a graph $G$ and $\\textrm{Hom}_\\Delta(H, G)$ denotes the number of homomorphisms from a connected graph $H$ on $h$ vertices to $G$ which map a particular vertex of $H$ to a vertex $v$ in $G$ with $d_v \\ge \\Delta$, then $ \\textrm{Hom}_\\Delta(H,G) \\le \\sum_{v\\in G} d_v^{h-1}\\mathbf{1}_{d_v\\ge \\Delta} $ We use this inequality to study the minimum sample size needed to estimate the number of copies of $H$ in $G$ by sampling vertices of $G$ at random.","url_abs":"https://arxiv.org/abs/2210.11336v1","url_pdf":"https://arxiv.org/pdf/2210.11336v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-note-on-estimating-global-subgraph-counts","repo_url":"https://github.com/valentas-kurauskas/subgraph-counts-hoeffding","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}