{"id":"https://openalex.org/W7156641118","doi":"https://doi.org/10.48550/arxiv.2604.23152","title":"Motif enrichment as a driver of scale-free behavior in rewired random regular graphs","display_name":"Motif enrichment as a driver of scale-free behavior in rewired random regular graphs","publication_year":2026,"publication_date":"2026-04-25","ids":{"openalex":"https://openalex.org/W7156641118","doi":"https://doi.org/10.48550/arxiv.2604.23152"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2604.23152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.23152","pdf_url":"https://arxiv.org/pdf/2604.23152","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2604.23152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044385266","display_name":"Pawat Akara-pipattana","orcid":"https://orcid.org/0009-0008-7124-5722","observed_orcids":["https://orcid.org/0009-0008-7124-5722"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Akara-pipattana, Pawat","raw_affiliation_strings":["LPTMS , CNRS - Universit\u00e9 Paris Saclay 91405 Orsay Cedex , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPTMS , CNRS - Universit\u00e9 Paris Saclay 91405 Orsay Cedex , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000367020","display_name":"Sergei Nechaev","orcid":"https://orcid.org/0000-0002-3268-9039","observed_orcids":["https://orcid.org/0000-0002-3268-9039"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES","FR"],"is_corresponding":false,"raw_author_name":"Nechaev, Sergei","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications (BIMSA) , Yanqi Lake , Huairou District , Beijing 101408 , China","LPTMS , CNRS - Universit\u00e9 Paris Saclay 91405 Orsay Cedex , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications (BIMSA) , Yanqi Lake , Huairou District , Beijing 101408 , China","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"LPTMS , CNRS - Universit\u00e9 Paris Saclay 91405 Orsay Cedex , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9907000064849854,"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":0.9907000064849854,"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":0.006599999964237213,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-regular-graphs","display_name":"random regular graphs","score":0.9340000152587891},{"id":"https://openalex.org/keywords/graph-rewiring","display_name":"graph rewiring","score":0.8640000224113464},{"id":"https://openalex.org/keywords/scale-free-networks","display_name":"scale-free networks","score":0.7490000128746033},{"id":"https://openalex.org/keywords/triangle-motifs","display_name":"triangle motifs","score":0.7919999957084656},{"id":"https://openalex.org/keywords/motif-enrichment","display_name":"motif enrichment","score":0.7739999890327454},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.8169999718666077},{"id":"https://openalex.org/keywords/fugacity","display_name":"fugacity","score":0.7799999713897705},{"id":"https://openalex.org/keywords/preferential-attachment","display_name":"preferential attachment","score":0.6570000052452087},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"degree distribution","score":0.7670000195503235},{"id":"https://openalex.org/keywords/isosceles-triangles","display_name":"isosceles triangles","score":0.7620000243186951},{"id":"https://openalex.org/keywords/efimov-states","display_name":"Efimov states","score":0.8489999771118164},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"mean-field theory","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6934999823570251},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.6126999855041504},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.5600000023841858},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5127000212669373},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5065000057220459},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5031999945640564},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.48179998993873596},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41499999165534973},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.29760000109672546},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.29179999232292175},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2671999931335449},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.2621000111103058},{"id":"https://openalex.org/C168907044","wikidata":"https://www.wikidata.org/wiki/Q7834431","display_name":"Transition point","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2604.23152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.23152","pdf_url":"https://arxiv.org/pdf/2604.23152","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.2604.23152","doi":"https://doi.org/10.48550/arxiv.2604.23152","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23152","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2604.23152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.23152","pdf_url":"https://arxiv.org/pdf/2604.23152","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7156641118.pdf","grobid_xml":"https://content.openalex.org/works/W7156641118.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2042634209","https://openalex.org/W2606001728","https://openalex.org/W3027372321","https://openalex.org/W3082642148","https://openalex.org/W4410314292","https://openalex.org/W2053812482","https://openalex.org/W1973569476","https://openalex.org/W4391258573","https://openalex.org/W4327810737","https://openalex.org/W7098078056"],"abstract_inverted_index":{"We":[0,81,136,164],"study":[1],"the":[2,15,23,27,32,54,61,71,78,86,91,97,127,130,150,157,173,180,184],"statistics":[3],"of":[4,18,29,56,60,73,88,93,126,129],"rewired":[5],"random":[6],"regular":[7],"graphs":[8],"(RRGs)":[9],"in":[10,52,69,103,200],"a":[11,40,48,65,100,110,116,161,191,201],"mixed":[12],"ensemble,":[13],"where":[14],"average":[16],"number":[17,28,55,72],"triangles":[19,57,74,169,196],"is":[20,58],"controlled":[21],"by":[22,84,109,115,146],"fugacity":[24,45],"$\u03bb$,":[25],"while":[26],"vertices":[30],"and":[31,133,155,179,197],"vertex":[33],"degree":[34,117],"are":[35,107,170],"fixed.":[36],"This":[37],"model":[38],"exhibits":[39],"phase":[41,50,67],"transition":[42],"at":[43],"critical":[44],"$\u03bb_{cr}$":[46,83],"from":[47],"triangle-poor":[49],"(TPP),":[51],"which":[53,70,104],"independent":[59,125],"system":[62,79,102],"size,":[63],"to":[64,140,183],"triangle-rich":[66],"(TRP),":[68],"scales":[75],"linearly":[76],"with":[77,90,122,172],"size.":[80],"estimate":[82],"comparing":[85],"entropy":[87],"TPP":[89],"energy":[92],"TRP.":[94],"Above":[95],"$\u03bb_{cr}$,":[96],"RRG":[98],"becomes":[99],"two-phase":[101],"dense":[105],"clusters":[106],"connected":[108],"sparse":[111],"scale-free":[112],"sub-network":[113],"characterized":[114],"distribution,":[118],"$P(d)":[119],"\\sim":[120],"d^{-\u03b3}$,":[121],"$\u03b3\\approx":[123],"2$,":[124],"size":[128],"whole":[131],"graph":[132],"its":[134,153],"degree.":[135],"attribute":[137],"this":[138],"behavior":[139],"an":[141],"\"emergent":[142],"preferential":[143],"attachment\"":[144],"induced":[145],"triangle":[147],"motifs,":[148],"describe":[149],"mechanism":[151],"underlying":[152],"formation,":[154],"derive":[156],"exponent":[158],"$\u03b3$":[159],"within":[160],"mean-field":[162],"approach.":[163],"show":[165],"that":[166],"most":[167],"inter-cluster":[168,185],"isosceles,":[171],"base":[174],"lying":[175],"inside":[176],"one":[177],"cluster":[178],"apex":[181],"belonging":[182],"network.":[186],"Finally,":[187],"we":[188],"speculate":[189],"on":[190],"possible":[192],"connection":[193],"between":[194],"these":[195],"Efimov":[198],"states":[199],"conformally":[202],"invariant":[203],"potential.":[204]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-04-29T00:00:00"}
