{"id":"https://openalex.org/W4416613028","doi":"https://doi.org/10.48550/arxiv.2505.23609","title":"The Generalized Skew Spectrum of Graphs","display_name":"The Generalized Skew Spectrum of Graphs","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4416613028","doi":"https://doi.org/10.48550/arxiv.2505.23609"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.23609","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.23609","pdf_url":"https://arxiv.org/pdf/2505.23609","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.23609","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014422500","display_name":"Armando Bellante","orcid":"https://orcid.org/0000-0003-2132-5798"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bellante, Armando","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081972979","display_name":"Martin Pl\u00e1vala","orcid":"https://orcid.org/0000-0002-3597-2702"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pl\u00e1vala, Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046199536","display_name":"Alessandro Luongo","orcid":"https://orcid.org/0000-0002-5746-3167"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luongo, Alessandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014422500"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.37439998984336853,"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"}},"topics":[{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.37439998984336853,"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"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.3203999996185303,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.05920000001788139,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/skew","display_name":"Skew","score":0.6632999777793884},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.505299985408783},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.41749998927116394},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.40939998626708984},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4092000126838684},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.40880000591278076},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.3792000114917755}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.6632999777793884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6176000237464905},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5120000243186951},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40310001373291016},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.31690001487731934},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.3142000138759613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28040000796318054},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.2678000032901764}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.23609","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.23609","pdf_url":"https://arxiv.org/pdf/2505.23609","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2505.23609","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.23609","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.23609","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.23609","pdf_url":"https://arxiv.org/pdf/2505.23609","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416613028.pdf","grobid_xml":"https://content.openalex.org/works/W4416613028.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,30,66,72],"family":[4,67],"of":[5,13,15,33,41,68,102],"permutation-invariant":[6],"graph":[7,34,44],"embeddings,":[8],"generalizing":[9],"the":[10,56,88,93,100],"Skew":[11,57,89],"Spectrum":[12,58],"graphs":[14],"Kondor":[16],"&":[17],"Borgwardt":[18],"(2008).":[19],"Grounded":[20],"in":[21],"group":[22],"theory":[23],"and":[24,39,52,77,111],"harmonic":[25],"analysis,":[26],"our":[27,103],"method":[28],"introduces":[29],"new":[31],"class":[32],"invariants":[35],"that":[36,70],"are":[37],"isomorphism-invariant":[38],"capable":[40],"embedding":[42],"richer":[43],"structures":[45],"-":[46,54],"including":[47],"attributed":[48],"graphs,":[49,51],"multilayer":[50],"hypergraphs":[53],"which":[55],"could":[59],"not":[60],"handle.":[61],"Our":[62],"generalization":[63],"further":[64],"defines":[65],"functions":[69],"enables":[71],"trade-off":[73],"between":[74],"computational":[75,95],"complexity":[76],"expressivity.":[78],"By":[79],"applying":[80],"generalization-preserving":[81],"heuristics":[82],"to":[83],"this":[84],"family,":[85],"we":[86],"improve":[87],"Spectrum's":[90],"expressivity":[91],"at":[92],"same":[94],"cost.":[96],"We":[97],"formally":[98],"prove":[99],"invariance":[101],"generalization,":[104],"demonstrate":[105],"its":[106,113],"improved":[107],"expressiveness":[108],"through":[109],"experiments,":[110],"discuss":[112],"efficient":[114],"computation.":[115]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}