{"id":"https://openalex.org/W3007912601","doi":"https://doi.org/10.1093/comnet/cnaa008","title":"Finite-size effects in exponential random graphs","display_name":"Finite-size effects in exponential random graphs","publication_year":2020,"publication_date":"2020-01-24","ids":{"openalex":"https://openalex.org/W3007912601","doi":"https://doi.org/10.1093/comnet/cnaa008","mag":"3007912601"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnaa008","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnaa008","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061217069","display_name":"A. Gorsky","orcid":"https://orcid.org/0000-0002-1619-3148"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A Gorsky","raw_affiliation_strings":["Institute for Information Transmission Problems RAS, Moscow, Russian Federation and Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems RAS, Moscow, Russian Federation and Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russian Federation","institution_ids":["https://openalex.org/I153845743","https://openalex.org/I4210107660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009318753","display_name":"Olga Valba","orcid":"https://orcid.org/0000-0003-0830-0166"},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"O Valba","raw_affiliation_strings":["Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russian Federation","institution_ids":["https://openalex.org/I118501908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009318753"],"corresponding_institution_ids":["https://openalex.org/I118501908"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.6675,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66500715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"8","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.996399998664856,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6895087957382202},{"id":"https://openalex.org/keywords/crossover","display_name":"Crossover","score":0.6760796308517456},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.6370266079902649},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5893415808677673},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.5680555105209351},{"id":"https://openalex.org/keywords/exponential-random-graph-models","display_name":"Exponential random graph models","score":0.5121610164642334},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49082431197166443},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.481440007686615},{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.47860878705978394},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4753941297531128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4110933244228363},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3920072317123413},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38723722100257874},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24663099646568298},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.122759610414505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07379266619682312}],"concepts":[{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6895087957382202},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.6760796308517456},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.6370266079902649},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5893415808677673},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5680555105209351},{"id":"https://openalex.org/C30549945","wikidata":"https://www.wikidata.org/wiki/Q5421526","display_name":"Exponential random graph models","level":4,"score":0.5121610164642334},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49082431197166443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.481440007686615},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.47860878705978394},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4753941297531128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4110933244228363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3920072317123413},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38723722100257874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24663099646568298},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.122759610414505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07379266619682312},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comnet/cnaa008","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnaa008","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2700558182","display_name":null,"funder_award_id":"20-01-041","funder_id":"https://openalex.org/F4320324261","funder_display_name":"National Research University Higher School of Economics"}],"funders":[{"id":"https://openalex.org/F4320324261","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1597577408","https://openalex.org/W1651399285","https://openalex.org/W1977990557","https://openalex.org/W2019258379","https://openalex.org/W2021884758","https://openalex.org/W2023196174","https://openalex.org/W2025241648","https://openalex.org/W2032746353","https://openalex.org/W2063499431","https://openalex.org/W2067190946","https://openalex.org/W2067247412","https://openalex.org/W2078578908","https://openalex.org/W2079634261","https://openalex.org/W2090275048","https://openalex.org/W2105575307","https://openalex.org/W2136525561","https://openalex.org/W2136931666","https://openalex.org/W2158345509","https://openalex.org/W2209760194","https://openalex.org/W2261699221","https://openalex.org/W2286096374","https://openalex.org/W2340811749","https://openalex.org/W2464785464","https://openalex.org/W2550203619","https://openalex.org/W2558082165","https://openalex.org/W2573615318","https://openalex.org/W2782669164","https://openalex.org/W2896446086","https://openalex.org/W2898088511","https://openalex.org/W2916078989","https://openalex.org/W2963553416","https://openalex.org/W2964329906","https://openalex.org/W2966111560","https://openalex.org/W3098067463","https://openalex.org/W3098789635","https://openalex.org/W3099640877","https://openalex.org/W3101241776","https://openalex.org/W3103690243","https://openalex.org/W3105028562","https://openalex.org/W3105554574","https://openalex.org/W6637181770","https://openalex.org/W6755916830","https://openalex.org/W6759252831"],"related_works":["https://openalex.org/W3102036813","https://openalex.org/W2600013268","https://openalex.org/W2359341608","https://openalex.org/W2806927426","https://openalex.org/W2597949273","https://openalex.org/W3007771191","https://openalex.org/W2154529522","https://openalex.org/W3106517793","https://openalex.org/W1967599767","https://openalex.org/W4299984326"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"we":[4],"show":[5],"numerically":[6],"the":[7,17,21,25,38,49,59,68,76,84,87,91,98,105,111,121],"strong":[8],"finite-size":[9],"effects":[10],"in":[11,90,104],"exponential":[12],"random":[13],"graphs.":[14],"Particularly,":[15],"for":[16,28,117],"two-star":[18],"model":[19],"above":[20],"critical":[22,60],"value":[23,61],"of":[24,41,62,64,97],"chemical":[26],"potential":[27],"triplets":[29],"a":[30,34,80],"ground":[31,69],"state":[32,70,85],"is":[33,115],"star-like":[35],"graph":[36],"with":[37],"finite":[39],"set":[40],"hubs":[42],"at":[43,52,102],"network":[44,77],"density":[45],"$p&amp;lt;0.5$":[46],"or":[47],"as":[48],"single":[50],"cluster":[51,81,99],"$p&amp;gt;0.5$.":[53],"We":[54,108],"find":[55],"that":[56,110],"there":[57],"exists":[58],"number":[63],"nodes":[65],"$N^{*}(p)$":[66],"when":[67],"undergoes":[71],"clear-cut":[72],"crossover.":[73],"At":[74],"$N&amp;gt;N^{*}(p),$":[75],"flows":[78],"via":[79],"evaporation":[82,96],"to":[83],"involving":[86],"small":[88],"star":[89],"Erd\u0151s\u2013R\u00e9nyi":[92],"environment.":[93],"The":[94],"similar":[95],"takes":[100],"place":[101],"$N&amp;gt;N^{*}(p)$":[103],"Strauss":[106],"model.":[107],"suggest":[109],"entropic":[112],"trap":[113],"mechanism":[114,119],"relevant":[116],"microscopic":[118],"behind":[120],"crossover":[122],"regime.":[123]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
