{"id":"https://openalex.org/W1606180716","doi":"https://doi.org/10.37236/935","title":"Component Evolution in Random Intersection Graphs","display_name":"Component Evolution in Random Intersection Graphs","publication_year":2007,"publication_date":"2007-01-29","ids":{"openalex":"https://openalex.org/W1606180716","doi":"https://doi.org/10.37236/935","mag":"1606180716"},"language":"en","primary_location":{"id":"doi:10.37236/935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r17/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040794392","display_name":"Michael Behrisch","orcid":"https://orcid.org/0000-0002-1102-103X"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Behrisch","raw_affiliation_strings":["Institut fr Informatik, Humboldt-Universitt zu Berlin, 10099 Berlin, Germany","Institut f\u00fcr Informatik, Humboldt-Universit\u00e4t zu Berlin, 10099 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut fr Informatik, Humboldt-Universitt zu Berlin, 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik, Humboldt-Universit\u00e4t zu Berlin, 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040794392"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":4.74,"has_fulltext":true,"cited_by_count":57,"citation_normalized_percentile":{"value":0.95580444,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","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":0.9991000294685364,"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":0.9991000294685364,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9952999949455261,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/giant-component","display_name":"Giant component","score":0.8128165006637573},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7973344922065735},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.7893558144569397},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7887697815895081},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.7174754738807678},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6996057033538818},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6350829601287842},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6022375226020813},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5088122487068176},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4405049979686737},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4212779104709625},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4149051010608673},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19357874989509583},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15658631920814514}],"concepts":[{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.8128165006637573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7973344922065735},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.7893558144569397},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7887697815895081},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.7174754738807678},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6996057033538818},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6350829601287842},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6022375226020813},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5088122487068176},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4405049979686737},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4212779104709625},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4149051010608673},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19357874989509583},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15658631920814514},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.293","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.293","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_14/PDF/v14i1r17.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4946944115","display_name":null,"funder_award_id":"Matheon","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1606180716.pdf","grobid_xml":"https://content.openalex.org/works/W1606180716.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1968481794","https://openalex.org/W1982442837","https://openalex.org/W1984679080","https://openalex.org/W1994697323","https://openalex.org/W1999360769","https://openalex.org/W1999803716","https://openalex.org/W2008052995","https://openalex.org/W2009483292","https://openalex.org/W2023212718","https://openalex.org/W2031211633","https://openalex.org/W2063346251","https://openalex.org/W2067112477","https://openalex.org/W2069091523","https://openalex.org/W2112976607","https://openalex.org/W2144589933","https://openalex.org/W2165064763","https://openalex.org/W2169015768","https://openalex.org/W2587442072","https://openalex.org/W3142570770","https://openalex.org/W3144881883","https://openalex.org/W4245852577","https://openalex.org/W4251418041","https://openalex.org/W6721489647"],"related_works":["https://openalex.org/W4293753062","https://openalex.org/W4287258775","https://openalex.org/W1889601917","https://openalex.org/W2142290020","https://openalex.org/W1606180716","https://openalex.org/W4293517767","https://openalex.org/W1585190875","https://openalex.org/W4308918461","https://openalex.org/W3126038111","https://openalex.org/W4286796120"],"abstract_inverted_index":{"We":[0,25,68],"study":[1],"the":[2,5,8,12,32,43,49,62],"evolution":[3],"of":[4,7,22,31,65,73],"order":[6,59],"largest":[9,64],"component":[10],"in":[11,40],"random":[13,34],"intersection":[14,35],"graph":[15],"model":[16],"which":[17],"reflects":[18],"some":[19],"clustering":[20],"properties":[21],"real\u2013world":[23],"networks.":[24],"show":[26],"that":[27,41],"for":[28],"appropriate":[29],"choice":[30],"parameters":[33],"graphs":[36],"differ":[37],"from":[38],"$G_{n,p}$":[39],"neither":[42],"so-called":[44],"giant":[45],"component,":[46],"appearing":[47],"when":[48],"expected":[50],"vertex":[51],"degree":[52],"gets":[53],"larger":[54],"than":[55],"one,":[56],"has":[57],"linear":[58],"nor":[60],"is":[61],"second":[63],"logarithmic":[66],"order.":[67],"also":[69],"describe":[70],"a":[71,77],"test":[72],"our":[74],"result":[75],"on":[76],"protein":[78],"similarity":[79],"network.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}