{"id":"https://openalex.org/W4392744233","doi":"https://doi.org/10.1007/s40747-024-01355-w","title":"A graph neural network with negative message passing and uniformity maximization for graph coloring","display_name":"A graph neural network with negative message passing and uniformity maximization for graph coloring","publication_year":2024,"publication_date":"2024-03-13","ids":{"openalex":"https://openalex.org/W4392744233","doi":"https://doi.org/10.1007/s40747-024-01355-w"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-024-01355-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-024-01355-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-024-01355-w.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-024-01355-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100369974","display_name":"Xiangyu Wang","orcid":"https://orcid.org/0000-0001-8718-6941"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I338023381","display_name":"Alexander von Humboldt Foundation","ror":"https://ror.org/012kf4317","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I338023381"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xiangyu Wang","raw_affiliation_strings":["Faculty of Technology, Bielefeld University, Germany","Alexander von Humboldt Professorship for Artificial Intelligence","Faculty of Technology, Bielefeld University, 33619 Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Technology, Bielefeld University, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"Alexander von Humboldt Professorship for Artificial Intelligence","institution_ids":["https://openalex.org/I338023381"]},{"raw_affiliation_string":"Faculty of Technology, Bielefeld University, 33619 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000979050","display_name":"Xueming Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I186272606","display_name":"Guangdong University of Foreign Studies","ror":"https://ror.org/00fhc9y79","country_code":"CN","type":"education","lineage":["https://openalex.org/I186272606"]},{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Xueming Yan","raw_affiliation_strings":["Faculty of Technology, Bielefeld University, 33619, Bielefeld, Germany","School of Information Science and Technology, Guangdong University of Foreign Studies, Guangzhou, 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Technology, Bielefeld University, 33619, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"School of Information Science and Technology, Guangdong University of Foreign Studies, Guangzhou, 510006, China","institution_ids":["https://openalex.org/I186272606"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032314861","display_name":"Yaochu Jin","orcid":"https://orcid.org/0000-0003-1100-0631"},"institutions":[{"id":"https://openalex.org/I3133055985","display_name":"Westlake University","ror":"https://ror.org/05hfa4n20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133055985"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yaochu Jin","raw_affiliation_strings":["School of Engineering, Westlake University, Hangzhou, 310030, China"],"raw_orcid":"https://orcid.org/0000-0003-1100-0631","affiliations":[{"raw_affiliation_string":"School of Engineering, Westlake University, Hangzhou, 310030, China","institution_ids":["https://openalex.org/I3133055985"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032314861"],"corresponding_institution_ids":["https://openalex.org/I3133055985"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1601,"currency":"EUR","value_usd":1726},"fwci":3.6425,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.93486451,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"4445","last_page":"4455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9872999787330627,"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":0.9872999787330627,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13991","display_name":"Nuclear Receptors and Signaling","score":0.9387000203132629,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.652081310749054},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6452770829200745},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5784709453582764},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5040806531906128},{"id":"https://openalex.org/keywords/message-passing","display_name":"Message passing","score":0.4657175540924072},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44745486974716187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43510064482688904},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34527385234832764}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.652081310749054},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6452770829200745},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5784709453582764},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5040806531906128},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.4657175540924072},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44745486974716187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43510064482688904},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34527385234832764},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s40747-024-01355-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-024-01355-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-024-01355-w.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0f49e370e938430d9271996cd0b1a338","is_oa":true,"landing_page_url":"https://doaj.org/article/0f49e370e938430d9271996cd0b1a338","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complex & Intelligent Systems, Vol 10, Iss 3, Pp 4445-4455 (2024)","raw_type":"article"},{"id":"pmh:oai:pub.uni-bielefeld.de:2988226","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:0070-pub-29882260","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"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":"","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"doi:10.1007/s40747-024-01355-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-024-01355-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-024-01355-w.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.4000000059604645}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323389","display_name":"Universit\u00e4t Bielefeld","ror":"https://ror.org/02hpadn98"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392744233.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1500067272","https://openalex.org/W1582334898","https://openalex.org/W1981276685","https://openalex.org/W2028140375","https://openalex.org/W2035773351","https://openalex.org/W2089189975","https://openalex.org/W2116341502","https://openalex.org/W2139906443","https://openalex.org/W2168000780","https://openalex.org/W2906943923","https://openalex.org/W2907492528","https://openalex.org/W2962810718","https://openalex.org/W2963382544","https://openalex.org/W2963465695","https://openalex.org/W2965857891","https://openalex.org/W2990761096","https://openalex.org/W3003265726","https://openalex.org/W3006129586","https://openalex.org/W3024182761","https://openalex.org/W3037845117","https://openalex.org/W3042856524","https://openalex.org/W3088578860","https://openalex.org/W3128443161","https://openalex.org/W3134315323","https://openalex.org/W3134509497","https://openalex.org/W3152893301","https://openalex.org/W3158196591","https://openalex.org/W4210462762","https://openalex.org/W4290876516","https://openalex.org/W4309830359","https://openalex.org/W6601065604","https://openalex.org/W6603599562","https://openalex.org/W6605533441","https://openalex.org/W6606425255","https://openalex.org/W6772184525","https://openalex.org/W6810999931","https://openalex.org/W6815235507","https://openalex.org/W6839257546"],"related_works":["https://openalex.org/W2978729728","https://openalex.org/W4288966080","https://openalex.org/W2510374584","https://openalex.org/W2134852660","https://openalex.org/W1530347314","https://openalex.org/W2901069556","https://openalex.org/W1556686321","https://openalex.org/W1902983110","https://openalex.org/W2390507337","https://openalex.org/W4389325792"],"abstract_inverted_index":{"Abstract":[0],"Graph":[1],"neural":[2,43,97,140,204],"networks":[3,44],"have":[4],"received":[5],"increased":[6],"attention":[7,52],"over":[8],"the":[9,81,114,120,129,132,139,155,161,171,198,201],"past":[10],"years":[11],"due":[12],"to":[13,17,45,56,127,144,169,192],"their":[14],"promising":[15],"ability":[16],"handle":[18],"graph-structured":[19],"data,":[20],"which":[21,71],"can":[22],"be":[23],"found":[24],"in":[25,84,104,113],"many":[26],"real-world":[27],"problems":[28,185],"such":[29],"as":[30],"recommender":[31],"systems":[32],"and":[33,49,186],"drug":[34],"synthesis.":[35],"Most":[36],"existing":[37],"research":[38],"focuses":[39],"on":[40,179],"using":[41],"graph":[42,65,69,86,96,106,173,183,203],"solve":[46],"homophilous":[47],"problems,":[48],"not":[50],"much":[51],"has":[53],"been":[54],"paid":[55],"heterophily-type":[57],"problems.":[58,78,108],"In":[59],"this":[60],"paper,":[61],"we":[62,88],"propose":[63],"a":[64,73,94,110],"network":[66,98,141],"model":[67,174],"for":[68,99,148],"coloring,":[70],"is":[72,125],"class":[74],"of":[75,123,131,135,200],"representative":[76],"heterophilous":[77],"Different":[79],"from":[80],"message":[82,91],"passing":[83,92],"conventional":[85],"networks,":[87],"introduce":[89],"negative":[90],"into":[93,118,160],"physics-inspired":[95],"more":[100,142],"effective":[101],"information":[102,121],"exchange":[103],"handling":[105],"coloring":[107,184],"Moreover,":[109],"new":[111],"term":[112],"objective":[115],"function":[116],"taking":[117],"account":[119],"entropy":[122],"nodes":[124],"suggested":[126],"increase":[128],"uniformity":[130],"color":[133],"assignment":[134],"each":[136,149],"node,":[137],"giving":[138],"chance":[143],"choose":[145],"suitable":[146],"colors":[147],"node.":[150],"Therefore,":[151],"it":[152],"could":[153],"avoid":[154],"final":[156],"solution":[157],"getting":[158],"stuck":[159],"local":[162],"optimum.":[163],"Experimental":[164],"studies":[165],"are":[166],"carried":[167],"out":[168],"compare":[170],"proposed":[172,202],"with":[175,190],"five":[176],"state-of-the-art":[177],"algorithms":[178],"ten":[180],"publicly":[181],"available":[182],"d":[187],"-regular":[188],"graphs":[189],"up":[191],"$$10^4$$":[193],"<mml:math":[194],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup></mml:math>":[195],"nodes,":[196],"demonstrating":[197],"effectiveness":[199],"network.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}