{"id":"https://openalex.org/W7140228467","doi":"https://doi.org/10.48550/arxiv.2603.20973","title":"Scaling laws in empirical networks","display_name":"Scaling laws in empirical networks","publication_year":2026,"publication_date":"2026-03-21","ids":{"openalex":"https://openalex.org/W7140228467","doi":"https://doi.org/10.48550/arxiv.2603.20973"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.20973","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20973","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,"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.20973","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Dutta, Upasana","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dutta, Upasana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ray, Alexander","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ray, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Clauset, Aaron","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clauset, Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.8973000049591064,"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":0.8973000049591064,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.019200000911951065,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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":0.015599999576807022,"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/assortativity","display_name":"Assortativity","score":0.8592000007629395},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6995999813079834},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.6976000070571899},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6723999977111816},{"id":"https://openalex.org/keywords/null-model","display_name":"Null model","score":0.6270999908447266},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.5486999750137329},{"id":"https://openalex.org/keywords/network-science","display_name":"Network science","score":0.4512999951839447},{"id":"https://openalex.org/keywords/network-model","display_name":"Network model","score":0.4449000060558319},{"id":"https://openalex.org/keywords/empirical-measure","display_name":"Empirical measure","score":0.44429999589920044},{"id":"https://openalex.org/keywords/scaling-law","display_name":"Scaling law","score":0.38510000705718994}],"concepts":[{"id":"https://openalex.org/C89694873","wikidata":"https://www.wikidata.org/wiki/Q4810299","display_name":"Assortativity","level":3,"score":0.8592000007629395},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6995999813079834},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6976000070571899},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6723999977111816},{"id":"https://openalex.org/C36382193","wikidata":"https://www.wikidata.org/wiki/Q7068966","display_name":"Null model","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.5486999750137329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47600001096725464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45669999718666077},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.4512999951839447},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C206654554","wikidata":"https://www.wikidata.org/wiki/Q5374247","display_name":"Empirical measure","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38580000400543213},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.38510000705718994},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C2988224531","wikidata":"https://www.wikidata.org/wiki/Q20830730","display_name":"Network structure","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35100001096725464},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.34549999237060547},{"id":"https://openalex.org/C53471067","wikidata":"https://www.wikidata.org/wiki/Q7574076","display_name":"Spatial network","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C28225019","wikidata":"https://www.wikidata.org/wiki/Q4915005","display_name":"Biological network","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.26759999990463257},{"id":"https://openalex.org/C68416499","wikidata":"https://www.wikidata.org/wiki/Q7001033","display_name":"Network formation","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C2779812341","wikidata":"https://www.wikidata.org/wiki/Q5891525","display_name":"Homophily","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C123757187","wikidata":"https://www.wikidata.org/wiki/Q9195957","display_name":"Network dynamics","level":2,"score":0.2590000033378601}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.20973","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20973","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.20973","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20973","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,"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":"Preprint"},"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":{"How":[0],"does":[1],"the":[2,24,65,117,170,190,196],"shape":[3],"of":[4,26,56,69,100,106,147,166,173,182,192,199],"a":[5,51,97,143,163],"network":[6,35,39,85,107,148,171,183],"change":[7],"as":[8],"its":[9],"size":[10,40],"increases?":[11],"Although":[12],"random":[13,44,129,140],"graph":[14,130],"models":[15,131,153,181],"provide":[16,176],"some":[17],"expectations":[18],"for":[19,180],"such":[20],"\"scaling":[21],"behaviors\"":[22],"in":[23,169,194],"structure":[25,36,156,172,198],"networks,":[27,71],"relatively":[28],"little":[29],"is":[30],"known":[31],"about":[32],"how":[33,42,73],"empirical":[34,48,66,122],"scales":[37],"with":[38,84,110,132,154],"or":[41],"well":[43],"graphs":[45,141],"explain":[46],"those":[47],"patterns.":[49],"Using":[50],"large,":[52],"structurally":[53],"diverse":[54],"corpus":[55],"networks":[57,90],"from":[58,91],"four":[59,93],"scientific":[60,94],"domains,":[61],"we":[62],"first":[63],"characterize":[64],"scaling":[67,101,112,123,149],"laws":[68,102,124],"real-world":[70],"considering":[72],"mean":[74,77],"degree,":[75],"transitivity,":[76],"geodesic":[78],"distance,":[79],"and":[80,185],"degree":[81],"assortativity":[82],"vary":[83],"size.":[86],"We":[87,114],"show":[88],"that":[89,137],"all":[92],"domains":[95],"exhibit":[96],"consistent":[98],"set":[99,165],"on":[103,189],"these":[104,121],"measures":[105],"structure,":[108,184],"but":[109],"differing":[111],"rates.":[113],"then":[115],"assess":[116],"extent":[118],"to":[119],"which":[120],"are":[125,142,157],"explained":[126],"by":[127],"three":[128],"different":[133],"structural":[134],"assumptions,":[135],"showing":[136],"configuration":[138],"model":[139,146],"remarkably":[144],"good":[145],"behavior,":[150],"although":[151],"null":[152],"modular":[155],"slightly":[158],"better.":[159],"These":[160],"findings":[161],"identify":[162],"new":[164,177,187],"common":[167],"patterns":[168],"complex":[174],"systems,":[175],"validation":[178],"targets":[179],"shed":[186],"light":[188],"role":[191],"randomness":[193],"shaping":[195],"large-scale":[197],"networks.":[200]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-25T00:00:00"}