{"id":"https://openalex.org/W7139954205","doi":"https://doi.org/10.48550/arxiv.2603.18452","title":"P\u00f3lya Thresholds Graphs","display_name":"P\u00f3lya Thresholds Graphs","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7139954205","doi":"https://doi.org/10.48550/arxiv.2603.18452"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.18452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18452","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.18452","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130249740","display_name":"Jinghan Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yu, Jinghan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065742137","display_name":"Fady Alajaji","orcid":"https://orcid.org/0000-0002-7980-724X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alajaji, Fady","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022064746","display_name":"Bahman Gharesifard","orcid":"https://orcid.org/0000-0003-1495-3489"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gharesifard, Bahman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5130249740"],"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.8220000267028809,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.8220000267028809,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.039400000125169754,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.014000000432133675,"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/adjacency-matrix","display_name":"Adjacency matrix","score":0.8119000196456909},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.7512000203132629},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5527999997138977},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5121999979019165},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48500001430511475},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4668999910354614},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42399999499320984},{"id":"https://openalex.org/keywords/degree-matrix","display_name":"Degree matrix","score":0.41609999537467957},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4050999879837036},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.39169999957084656}],"concepts":[{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.8119000196456909},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.7512000203132629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7111999988555908},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5527999997138977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5178999900817871},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5121999979019165},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4668999910354614},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43860000371932983},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42399999499320984},{"id":"https://openalex.org/C162199024","wikidata":"https://www.wikidata.org/wiki/Q3085391","display_name":"Degree matrix","level":5,"score":0.41609999537467957},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.3864000141620636},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.367900013923645},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3617999851703644},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C25799778","wikidata":"https://www.wikidata.org/wiki/Q4724003","display_name":"Algebraic graph theory","level":3,"score":0.3005000054836273},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.289900004863739},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.2721000015735626},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.26669999957084656},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.18452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18452","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":"doi:10.48550/arxiv.2603.18452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18452","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":false,"raw_source_name":null,"raw_type":"article"},"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":{"We":[0],"introduce":[1],"the":[2,39,87,91,94,100,130,136,140],"P\u00f3lya":[3,24,95,168],"threshold":[4,16,73,142,169],"graph":[5,17,74],"model":[6],"and":[7,11,59,111,121,151],"derive":[8,99],"its":[9,109,127,149],"stochastic":[10],"algebraic":[12,131],"properties.":[13],"This":[14,68],"random":[15,72,141],"is":[18,52],"generated":[19],"sequentially":[20],"via":[21],"a":[22,36,48,71,116,145],"two-color":[23],"urn":[25,40],"process.":[26],"Starting":[27],"from":[28,38],"an":[29,43,76,81,123,156],"empty":[30],"graph,":[31,143],"each":[32],"time":[33],"step":[34],"involves":[35],"draw":[37,88,96],"that":[41,79],"produces":[42],"indicator":[44],"variable,":[45],"determining":[46],"whether":[47],"newly":[49],"added":[50],"node":[51],"universal":[53],"(connected":[54,63],"to":[55,64],"all":[56],"existing":[57,66],"nodes":[58],"itself)":[60],"or":[61],"isolated":[62],"no":[65],"nodes).":[67],"construction":[69],"yields":[70],"with":[75],"adjacency":[77],"matrix":[78,138],"admits":[80],"explicit":[82,124],"representation":[83],"in":[84],"terms":[85],"of":[86,93,139,148,158],"sequence.":[89],"Using":[90],"structure":[92],"process,":[97],"we":[98,114,133,162],"exact":[101],"degree":[102],"distribution":[103],"for":[104,126],"any":[105],"arbitrary":[106],"node,":[107],"including":[108],"mean":[110],"variance.":[112],"Furthermore,":[113],"evaluate":[115],"distance-based":[117],"decay":[118],"centrality":[119],"score":[120],"provide":[122],"expression":[125],"expectation.":[128],"On":[129],"side,":[132],"explicitly":[134],"characterize":[135],"Laplacian":[137],"obtaining":[144],"closed-form":[146],"description":[147],"spectrum":[150],"corresponding":[152],"eigenbasis.":[153],"Finally,":[154],"as":[155],"application":[157],"these":[159],"structural":[160],"results,":[161],"analyze":[163],"discrete-time":[164],"consensus":[165],"dynamics":[166],"on":[167],"graphs.":[170]},"counts_by_year":[],"updated_date":"2026-03-21T06:36:02.116451","created_date":"2026-03-21T00:00:00"}
