{"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/graph-homomorphism-convolution","title":"Graph Homomorphism Convolution","arxiv_id":"2005.01214","date":"2020-05-03","proceeding":"ICML 2020 1","authors":["Hoang NT","Takanori Maehara"],"abstract":"In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $\\mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $\\mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $\\mathcal{F}$-invariant functions. In practice, by choosing $\\mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods.","url_abs":"https://arxiv.org/abs/2005.01214v2","url_pdf":"https://arxiv.org/pdf/2005.01214v2.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":"abstracts"},"code_links":[{"paper_slug":"graph-homomorphism-convolution","repo_url":"https://github.com/gear/graph-homomorphism-network","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"graph-classification","task_name":"Graph Classification"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2005.01214","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2005.01214"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/gear/graph-homomorphism-network","reach":null}],"summary":{"ran_draft_wrong":2,"unverified":1},"by_repo_kind":{"listed":{"samples":3,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"0a8ef2ff5c39e2e9","entry":"hom_tree","repo":"gear/graph-homomorphism-network","repo_kind":"listed","path":"src/ghc/homomorphism.py","file_url":"https://github.com/gear/graph-homomorphism-network/blob/HEAD/src/ghc/homomorphism.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0a8ef2ff5c39e2e9"}},{"code_sha256_prefix":"d169a8872cb998b8","entry":"hom_tree_labeled","repo":"gear/graph-homomorphism-network","repo_kind":"listed","path":"src/ghc/homomorphism.py","file_url":"https://github.com/gear/graph-homomorphism-network/blob/HEAD/src/ghc/homomorphism.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d169a8872cb998b8"}},{"code_sha256_prefix":"541f29f4f6d9e50e","entry":"hom_tree_explabeled","repo":"gear/graph-homomorphism-network","repo_kind":"listed","path":"src/ghc/homomorphism.py","file_url":"https://github.com/gear/graph-homomorphism-network/blob/HEAD/src/ghc/homomorphism.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"541f29f4f6d9e50e"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}