{"id":"https://openalex.org/W2725812641","doi":"https://doi.org/10.1137/17m1138303","title":"The Distribution of Minimum-Weight Cliques and Other Subgraphs in Graphs with Random Edge Weights","display_name":"The Distribution of Minimum-Weight Cliques and Other Subgraphs in Graphs with Random Edge Weights","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2725812641","doi":"https://doi.org/10.1137/17m1138303","mag":"2725812641"},"language":"en","primary_location":{"id":"doi:10.1137/17m1138303","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138303","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1606.04925","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan Frieze","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054318475","display_name":"Wesley Pegden","orcid":"https://orcid.org/0000-0002-3680-1817"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wesley Pegden","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083890565","display_name":"Gregory B. Sorkin","orcid":"https://orcid.org/0000-0003-4935-7820"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gregory B. Sorkin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5636,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55373464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"3","first_page":"2115","last_page":"2133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7609958648681641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.75173020362854},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.7367965579032898},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.708844780921936},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.6006948947906494},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.5661545991897583},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.5430031418800354},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5107839107513428},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5002157688140869},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.47596949338912964},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.45665279030799866},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.24125328660011292},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.13363367319107056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12375101447105408},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.11088904738426208}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7609958648681641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.75173020362854},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.7367965579032898},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.708844780921936},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.6006948947906494},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.5661545991897583},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5430031418800354},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5107839107513428},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5002157688140869},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.47596949338912964},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.45665279030799866},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.24125328660011292},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.13363367319107056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12375101447105408},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.11088904738426208},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1138303","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138303","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.04925","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.04925","pdf_url":"https://arxiv.org/pdf/1606.04925","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.lse.ac.uk:87660","is_oa":true,"landing_page_url":"https://orcid.org/0000-0003-4935-7820>","pdf_url":"http://eprints.lse.ac.uk/87660/1/Sorkin_Distribution%20of%20Minimum-Weight%20Cliques.pdf","source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"mag:2725812641","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.04925","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1606.04925","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.04925","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1606.04925","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.04925","pdf_url":"https://arxiv.org/pdf/1606.04925","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1487637096","display_name":null,"funder_award_id":"DMS1362785","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W836939274","https://openalex.org/W2016966047","https://openalex.org/W2069699650","https://openalex.org/W2090430963","https://openalex.org/W2141369175","https://openalex.org/W2336317531","https://openalex.org/W2905110430","https://openalex.org/W4230964139"],"related_works":["https://openalex.org/W2952026483","https://openalex.org/W3008300036","https://openalex.org/W3212733298","https://openalex.org/W2251198337","https://openalex.org/W3194337630","https://openalex.org/W2049956324","https://openalex.org/W2964417322","https://openalex.org/W2011121646","https://openalex.org/W1984128946","https://openalex.org/W2033897500","https://openalex.org/W1564693713","https://openalex.org/W3041562587","https://openalex.org/W2036312115","https://openalex.org/W2143305437","https://openalex.org/W2083618772","https://openalex.org/W3100146268","https://openalex.org/W2951956857","https://openalex.org/W2168287904","https://openalex.org/W1999514338","https://openalex.org/W2613250177"],"abstract_inverted_index":{"We":[0,85],"determine,":[1],"asymptotically":[2],"in":[3,22,58,68,113],"$n$,":[4],"the":[5,10,36,44,53,64,87,120],"distribution":[6,38,56],"and":[7,67,81,95],"mean":[8],"of":[9,12,93,109],"weight":[11],"a":[13,23,59,69,110,114],"minimum-weight":[14,107],"$k$-clique":[15],"(or":[16],"any":[17],"strictly":[18],"balanced":[19],"graph":[20,25,111],"$H$)":[21],"complete":[24],"$K_n$":[26],"whose":[27],"edge":[28,122],"weights":[29,123],"are":[30,124],"independent":[31],"random":[32],"values":[33,92],"drawn":[34],"from":[35,63],"uniform":[37],"or":[39],"other":[40,79,82],"continuous":[41],"distributions.":[42,84],"For":[43],"clique,":[45],"we":[46],"also":[47],"provide":[48],"explicit":[49],"(nonasymptotic)":[50],"bounds":[51],"on":[52],"distribution's":[54],"cumulative":[55],"function":[57],"form":[60,76],"obtained":[61],"directly":[62],"Stein--Chen":[65],"method":[66],"looser":[70],"but":[71,128],"simpler":[72],"form.":[73],"The":[74,97],"direct":[75],"extends":[77],"to":[78,102],"subgraphs":[80],"edge-weight":[83],"illustrate":[86],"clique":[88],"results":[89,98],"for":[90],"various":[91],"$k$":[94],"$n$.":[96],"may":[99],"be":[100],"applied":[101],"evaluate":[103],"whether":[104],"an":[105],"observed":[106],"copy":[108],"$H$":[112],"network":[115],"provides":[116],"statistical":[117],"evidence":[118],"that":[119],"network's":[121],"not":[125],"independently":[126],"distributed":[127],"have":[129],"some":[130],"structure.":[131]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}