{"id":"https://openalex.org/W7163985514","doi":"https://doi.org/10.48550/arxiv.2606.09484","title":"Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism","display_name":"Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism","publication_year":2026,"publication_date":"2026-06-08","ids":{"openalex":"https://openalex.org/W7163985514","doi":"https://doi.org/10.48550/arxiv.2606.09484"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.09484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.09484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126225370","display_name":"Kumar Thushalika","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thushalika, Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138216752","display_name":"Sukumar Kishanthan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kishanthan, Sukumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138219246","display_name":"Asela Hevapathige","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hevapathige, Asela","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.8151000142097473,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.8151000142097473,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.06459999829530716,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.024000000208616257,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.6693999767303467},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5235999822616577},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.47429999709129333},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.46140000224113464},{"id":"https://openalex.org/keywords/subgraph-isomorphism-problem","display_name":"Subgraph isomorphism problem","score":0.4043000042438507},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.4023999869823456}],"concepts":[{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.6693999767303467},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5235999822616577},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49549999833106995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47909998893737793},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.47429999709129333},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.46140000224113464},{"id":"https://openalex.org/C131992880","wikidata":"https://www.wikidata.org/wiki/Q2528185","display_name":"Subgraph isomorphism problem","level":3,"score":0.4043000042438507},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.4023999869823456},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.2964000105857849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.289900004863739},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.2685999870300293}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.09484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.09484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large":[0],"language":[1],"models":[2],"(LLMs)":[3],"have":[4],"shown":[5],"impressive":[6],"performance":[7,48],"on":[8,42,96],"diverse":[9],"reasoning":[10,17,75,98],"tasks,":[11],"yet":[12],"their":[13,64],"capacity":[14],"for":[15,87],"structural":[16,89],"in":[18,34],"graphs":[19,53],"remains":[20],"unclear.":[21],"We":[22],"investigate":[23],"whether":[24],"LLMs":[25,38,60,70],"can":[26],"genuinely":[27],"understand":[28],"graph":[29,35,78,97],"isomorphism":[30,43],"-a":[31],"fundamental":[32,85],"problem":[33],"theory.":[36],"While":[37],"achieve":[39],"near-perfect":[40],"accuracy":[41],"detection,":[44],"we":[45],"show":[46],"this":[47],"is":[49,83],"illusory.":[50],"When":[51],"identical":[52],"are":[54],"presented":[55],"with":[56],"permuted":[57],"node":[58],"labels,":[59],"fail":[61],"to":[62],"identify":[63],"isomorphism.":[65],"This":[66],"finding":[67],"suggests":[68],"that":[69,94],"exploit":[71],"patterns":[72],"rather":[73],"than":[74],"about":[76],"abstract":[77],"structure.":[79],"Since":[80],"permutation":[81],"invariance":[82],"a":[84],"requirement":[86],"valid":[88],"reasoning,":[90],"these":[91],"results":[92],"indicate":[93],"success":[95],"benchmarks":[99],"should":[100],"not":[101],"be":[102],"interpreted":[103],"as":[104],"evidence":[105],"of":[106],"genuine":[107],"topological":[108],"understanding.":[109]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-10T00:00:00"}
