{"id":"https://openalex.org/W7207809697","doi":"https://doi.org/10.48550/arxiv.2609.01624","title":"Higher-order rich clubs and configuration models on general directed hypergraphs","display_name":"Higher-order rich clubs and configuration models on general directed hypergraphs","publication_year":2026,"publication_date":"2026-08-03","ids":{"openalex":"https://openalex.org/W7207809697","doi":"https://doi.org/10.48550/arxiv.2609.01624"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01624","pdf_url":"https://arxiv.org/pdf/2609.01624","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2609.01624","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149897619","display_name":"Jason P. Smith","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I52590639","display_name":"Nottingham Trent University","ror":"https://ror.org/04xyxjd90","country_code":"GB","type":"education","lineage":["https://openalex.org/I52590639"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Smith, Jason P.","raw_affiliation_strings":["Department of Physical Sciences , Nottingham Trent University , Nottingham , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical Sciences , Nottingham Trent University , Nottingham , UK","institution_ids":["https://openalex.org/I52590639"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062493847","display_name":"Celia Hacker","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hacker, Celia","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences , Leipzig , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences , Leipzig , Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003295156","display_name":"J\u0101nis Lazovskis","orcid":"https://orcid.org/0000-0002-3285-7522","observed_orcids":["https://orcid.org/0000-0002-3285-7522"]},"institutions":[{"id":"https://openalex.org/I91123046","display_name":"University of Latvia","ror":"https://ror.org/05g3mes96","country_code":"LV","type":"education","lineage":["https://openalex.org/I91123046"]}],"countries":["LV"],"is_corresponding":false,"raw_author_name":"Lazovskis, J\u0101nis","raw_affiliation_strings":["Institute of Clinical and Preventive Medicine , University of Latvia , Riga , Latvia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Clinical and Preventive Medicine , University of Latvia , Riga , Latvia","institution_ids":["https://openalex.org/I91123046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003880446","display_name":"Florian Unger","orcid":"https://orcid.org/0000-0003-3371-0335","observed_orcids":["https://orcid.org/0000-0003-3371-0335"]},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Unger, Florian","raw_affiliation_strings":["Graz University of Technology , Graz , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graz University of Technology , Graz , Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002330647","display_name":"Keith Smith","orcid":"https://orcid.org/0000-0002-4615-9020","observed_orcids":["https://orcid.org/0000-0002-4615-9020"]},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Smith, Keith M.","raw_affiliation_strings":["Computer and Information Sciences , University of Strathclyde , Glasgow , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer and Information Sciences , University of Strathclyde , Glasgow , UK","institution_ids":["https://openalex.org/I181647926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023858922","display_name":"Daniela Egas Santander","orcid":"https://orcid.org/0000-0001-9838-7992","observed_orcids":["https://orcid.org/0000-0001-9838-7992"]},"institutions":[{"id":"https://openalex.org/I4210148197","display_name":"Center for Systems Biology Dresden","ror":"https://ror.org/05hrn3e05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210111875","https://openalex.org/I4210148197","https://openalex.org/I4210159854","https://openalex.org/I78650965"]},{"id":"https://openalex.org/I4210159854","display_name":"Max Planck Institute of Molecular Cell Biology and Genetics","ror":"https://ror.org/05b8d3w18","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210159854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Santander, Daniela Egas","raw_affiliation_strings":["Center for Systems Biology Dresden (CSBD) , Dresden , Germany","Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG) , Dresden , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Systems Biology Dresden (CSBD) , Dresden , Germany","institution_ids":["https://openalex.org/I4210148197"]},{"raw_affiliation_string":"Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG) , Dresden , Germany","institution_ids":["https://openalex.org/I4210159854"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"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":0.9990000128746033,"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":0.9990000128746033,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0003000000142492354,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/higher-order-interactions","display_name":"higher-order interactions","score":0.8009999990463257},{"id":"https://openalex.org/keywords/directed-hypergraphs","display_name":"directed hypergraphs","score":0.9369999766349792},{"id":"https://openalex.org/keywords/configuration-model","display_name":"configuration model","score":0.7639999985694885},{"id":"https://openalex.org/keywords/complex-networks","display_name":"complex networks","score":0.6809999942779541},{"id":"https://openalex.org/keywords/connectome","display_name":"connectome","score":0.6959999799728394},{"id":"https://openalex.org/keywords/dynamic-networks","display_name":"dynamic networks","score":0.8349999785423279},{"id":"https://openalex.org/keywords/disease-transmission","display_name":"disease transmission","score":0.8360000252723694},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.6990000009536743}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7425000071525574},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6783000230789185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4551999866962433},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4433000087738037},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4196999967098236},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41499999165534973},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36329999566078186},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.2874000072479248},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01624","pdf_url":"https://arxiv.org/pdf/2609.01624","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.01624","doi":"https://doi.org/10.48550/arxiv.2609.01624","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01624","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01624","pdf_url":"https://arxiv.org/pdf/2609.01624","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2248961877","display_name":null,"funder_award_id":"1.1.1.9/LZP/1/24/125","funder_id":"https://openalex.org/F4320323269","funder_display_name":"Latvijas Zin\u0101tnes Padome"},{"id":"https://openalex.org/G3485588089","display_name":"Random Models of Directed Simplicial Complexes","funder_award_id":"UKRI171","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320323269","display_name":"Latvijas Zin\u0101tnes Padome","ror":"https://ror.org/02ar66p97"},{"id":"https://openalex.org/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https://ror.org/00ez2he07"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207809697.pdf","grobid_xml":"https://content.openalex.org/works/W7207809697.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4404089431","https://openalex.org/W2792350283","https://openalex.org/W2953542473","https://openalex.org/W7140182339","https://openalex.org/W3125671098","https://openalex.org/W4392971611","https://openalex.org/W3190196337","https://openalex.org/W4393381856","https://openalex.org/W4378364543","https://openalex.org/W4310060722"],"abstract_inverted_index":{"Detecting":[0],"structure":[1,63,212,240],"in":[2,107,213,236],"complex":[3,68],"networks,":[4],"especially":[5],"those":[6,36],"arising":[7],"from":[8,140],"physical":[9],"systems,":[10],"is":[11,20],"a":[12,30,72,108,160],"central":[13,79],"problem":[14],"across":[15],"the":[16,62,97,171,183,195,208,232,241],"sciences.":[17],"One":[18],"approach":[19,49],"via":[21],"rich":[22,185,244],"club":[23,74,162,186,245],"analysis,":[24],"which":[25,94,113],"identifies":[26],"important":[27],"vertices":[28,37,80],"using":[29],"centrality":[31],"metric":[32],"and":[33,64,129,190,193,231],"measures":[34],"whether":[35,78],"are":[38,81],"more":[39,82],"tightly":[40,83],"interconnected":[41,84],"than":[42,85],"expected":[43,86],"by":[44,87,215],"chance.":[45],"While":[46],"informative,":[47],"this":[48],"captures":[50],"only":[51],"pairwise":[52],"interactions,":[53,93],"missing":[54],"out":[55],"on":[56,168],"higher-order":[57,92],"ones":[58],"known":[59],"to":[60,136,176],"shape":[61],"function":[65],"of":[66,99,111,149,202,218,225,229],"many":[67],"systems.":[69],"We":[70,105,205],"propose":[71],"hyper-rich":[73,161],"pipeline":[75,209],"that":[76,119,207],"asks":[77],"chance":[88],"through":[89],"hyperedges":[90],"encoding":[91],"also":[95],"enables":[96],"inclusion":[98],"important,":[100],"often":[101],"omitted,":[102],"directional":[103],"information.":[104],"work":[106],"broad":[109],"class":[110],"hypergraphs,":[112,118,125,128,192],"we":[114,158],"call":[115],"general":[116],"directed":[117,127,137,150,203],"includes":[120],"as":[121],"special":[122],"cases":[123],"undirected":[124,191],"head-and-tail":[126],"totally":[130],"ordered":[131],"hypergraphs":[132,157],"(a":[133],"hypergraph":[134,151,234],"related":[135],"simplicial":[138],"complexes":[139],"topological":[141],"data":[142,214],"analysis).":[143],"This":[144],"unifies":[145],"several":[146],"non-equivalent":[147],"notions":[148,187],"under":[152],"one":[153],"definition.":[154],"On":[155],"these":[156],"define":[159],"framework":[163],"whose":[164],"concrete":[165],"construction":[166],"depends":[167],"explicit":[169],"choices":[170,181],"domain":[172],"scientist":[173],"fixes":[174],"according":[175],"their":[177],"research":[178],"goals.":[179],"Particular":[180],"recover":[182],"existing":[184],"for":[188,199],"graphs":[189],"yield":[194],"first":[196],"such":[197],"notion":[198],"each":[200,237],"version":[201],"hypergraphs.":[204],"demonstrate":[206],"recovers":[210],"meaningful":[211],"studying":[216],"networks":[217,224,228],"very":[219],"different":[220],"origins:":[221],"connectomes,":[222],"temporal":[223],"infectious":[226],"spread,":[227],"poems,":[230],"XGI":[233],"database,":[235],"case":[238],"detecting":[239],"standard":[242],"graph":[243],"misses.":[246]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}
