{"id":"https://openalex.org/W1985339741","doi":"https://doi.org/10.1103/physreve.85.056109","title":"Community structure and scale-free collections of Erd\u0151s-R\u00e9nyi graphs","display_name":"Community structure and scale-free collections of Erd\u0151s-R\u00e9nyi graphs","publication_year":2012,"publication_date":"2012-05-10","ids":{"openalex":"https://openalex.org/W1985339741","doi":"https://doi.org/10.1103/physreve.85.056109","mag":"1985339741","pmid":"https://pubmed.ncbi.nlm.nih.gov/23004823"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.85.056109","doi":"https://doi.org/10.1103/physreve.85.056109","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.85.056109","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1112.3644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038687804","display_name":"Comandur Seshadhri","orcid":"https://orcid.org/0000-0003-2163-3555","observed_orcids":["https://orcid.org/0000-0003-2163-3555"]},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Seshadhri","raw_affiliation_strings":["Sandia National Laboratories, Livermore, California 94551, USA. scomand@sandia.gov","Sandia National Laboratories, Livermore, California 94551, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories, Livermore, California 94551, USA. scomand@sandia.gov","institution_ids":["https://openalex.org/I192454743"]},{"raw_affiliation_string":"Sandia National Laboratories, Livermore, California 94551, USA","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039127251","display_name":"Tamara G. Kolda","orcid":"https://orcid.org/0000-0003-4176-2493","observed_orcids":["https://orcid.org/0000-0003-4176-2493"]},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamara G. Kolda","raw_affiliation_strings":["Sandia National Laboratories, Livermore, California 94551, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories, Livermore, California 94551, USA","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101869106","display_name":"Ali Pinar","orcid":"https://orcid.org/0000-0002-9164-7808","observed_orcids":["https://orcid.org/0000-0002-9164-7808"]},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Pinar","raw_affiliation_strings":["Sandia National Laboratories, Livermore, California 94551, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories, Livermore, California 94551, USA","institution_ids":["https://openalex.org/I192454743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I192454743"],"apc_list":null,"apc_paid":null,"fwci":15.3594,"has_fulltext":false,"cited_by_count":244,"citation_normalized_percentile":{"value":0.9945306,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"85","issue":"5","first_page":"056109","last_page":"056109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":1.0,"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":1.0,"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":0.0,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/community-structure","display_name":"community structure","score":0.9950000047683716},{"id":"https://openalex.org/keywords/erdos-renyi-graphs","display_name":"Erd\u0151s-R\u00e9nyi random graphs","score":0.9629999995231628},{"id":"https://openalex.org/keywords/scale-free-networks","display_name":"scale-free networks","score":0.8679999709129333},{"id":"https://openalex.org/keywords/dense-subgraphs","display_name":"dense subgraphs","score":0.8270000219345093},{"id":"https://openalex.org/keywords/heavy-tailed-degree-distribution","display_name":"heavy-tailed degree distribution","score":0.9359999895095825},{"id":"https://openalex.org/keywords/social-networks","display_name":"social networks","score":0.7620000243186951}],"concepts":[{"id":"https://openalex.org/C133079900","wikidata":"https://www.wikidata.org/wiki/Q5155065","display_name":"Community structure","level":2,"score":0.5105534791946411},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.49452587962150574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4137304425239563},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3643147349357605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34891849756240845},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.24150040745735168},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.09218767285346985}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/physreve.85.056109","doi":"https://doi.org/10.1103/physreve.85.056109","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.85.056109","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:23004823","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23004823","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1112.3644","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.3644","pdf_url":"https://arxiv.org/pdf/1112.3644","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.1112.3644","doi":"https://doi.org/10.48550/arxiv.1112.3644","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1112.3644","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1112.3644","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.3644","pdf_url":"https://arxiv.org/pdf/1112.3644","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1482680420","https://openalex.org/W1534511119","https://openalex.org/W1560267311","https://openalex.org/W1848620603","https://openalex.org/W1928223220","https://openalex.org/W1971215074","https://openalex.org/W1971421925","https://openalex.org/W1980940295","https://openalex.org/W1990495065","https://openalex.org/W1991306266","https://openalex.org/W2000042664","https://openalex.org/W2008620264","https://openalex.org/W2016194249","https://openalex.org/W2020385058","https://openalex.org/W2023655578","https://openalex.org/W2027377866","https://openalex.org/W2029130073","https://openalex.org/W2037859435","https://openalex.org/W2047940964","https://openalex.org/W2064274783","https://openalex.org/W2067247412","https://openalex.org/W2070265204","https://openalex.org/W2076688688","https://openalex.org/W2084478247","https://openalex.org/W2084573744","https://openalex.org/W2085761620","https://openalex.org/W2101267973","https://openalex.org/W2108614537","https://openalex.org/W2110620844","https://openalex.org/W2112090702","https://openalex.org/W2112681514","https://openalex.org/W2112976607","https://openalex.org/W2115579680","https://openalex.org/W2119998616","https://openalex.org/W2123736933","https://openalex.org/W2146591355","https://openalex.org/W2151936673","https://openalex.org/W2157082398","https://openalex.org/W2157762631","https://openalex.org/W2260674112","https://openalex.org/W2573956962","https://openalex.org/W2593860074","https://openalex.org/W3103362336","https://openalex.org/W3136243343","https://openalex.org/W3143219376","https://openalex.org/W4247388812","https://openalex.org/W4312512934"],"related_works":["https://openalex.org/W4206851556","https://openalex.org/W2088240926","https://openalex.org/W7098232124","https://openalex.org/W2028314260","https://openalex.org/W2886350584","https://openalex.org/W2028201018","https://openalex.org/W7096284057","https://openalex.org/W2535608133","https://openalex.org/W3102058415","https://openalex.org/W7095591804"],"abstract_inverted_index":{"Community":[0],"structure":[1,17,81],"plays":[2],"a":[3,31,35,60,75,84],"significant":[4],"role":[5],"in":[6],"the":[7,103,115],"analysis":[8],"of":[9,50,87,118],"social":[10,121],"networks":[11],"and":[12,21,42,79,109],"similar":[13],"graphs,":[14],"yet":[15],"this":[16],"is":[18,38],"little":[19],"understood":[20],"not":[22],"well":[23,95],"captured":[24],"by":[25],"most":[26],"models.":[27],"We":[28,47],"formally":[29],"define":[30],"community":[32,57,80],"to":[33,52],"be":[34],"subgraph":[36],"that":[37,54,71,111],"internally":[39],"highly":[40],"connected":[41],"has":[43],"no":[44],"deeper":[45],"substructure.":[46],"use":[48],"tools":[49],"combinatorics":[51],"show":[53],"any":[55,72],"such":[56],"must":[58,82],"contain":[59,83],"dense":[61,88],"Erd\u0151s-R\u00e9nyi":[62,106],"(ER)":[63],"subgraph.":[64],"Based":[65],"on":[66],"mathematical":[67],"arguments,":[68],"we":[69,101],"hypothesize":[70],"graph":[73],"with":[74,96],"heavy-tailed":[76],"degree":[77],"distribution":[78],"scale-free":[85],"collection":[86],"ER":[89],"subgraphs.":[90],"These":[91],"theoretical":[92],"observations":[93],"corroborate":[94],"empirical":[97],"evidence.":[98],"From":[99],"this,":[100],"propose":[102],"Block":[104],"Two-Level":[105],"(BTER)":[107],"model,":[108],"demonstrate":[110],"it":[112],"accurately":[113],"captures":[114],"observable":[116],"properties":[117],"many":[119],"real-world":[120],"networks.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":31},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}