{"id":"https://openalex.org/W2964728636","doi":null,"title":"Higher order degree in simplicial complexes, multi combinatorial Laplacian and applications of TDA to complex networks","display_name":"Higher order degree in simplicial complexes, multi combinatorial Laplacian and applications of TDA to complex networks","publication_year":2019,"publication_date":"2019-08-02","ids":{"openalex":"https://openalex.org/W2964728636","mag":"2964728636"},"language":"en","primary_location":{"id":"mag:2964728636","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.02583","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1908.02583","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020291956","display_name":"Daniel Hern\u00e1ndez Serrano","orcid":"https://orcid.org/0000-0002-2467-3010","observed_orcids":["https://orcid.org/0000-0002-2467-3010"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Hern\u00e1ndez Serrano","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2467-3010","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091493882","display_name":"Dar\u00edo S\u00e1nchez G\u00f3mez","orcid":"https://orcid.org/0000-0002-4521-2758","observed_orcids":["https://orcid.org/0000-0002-4521-2758"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dar\u00edo S\u00e1nchez G\u00f3mez","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4521-2758","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":5,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9937000274658203,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9937000274658203,"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"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.0013000000035390258,"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/T11476","display_name":"Graph theory and applications","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.9549999833106995},{"id":"https://openalex.org/keywords/combinatorial-laplacian","display_name":"combinatorial Laplacian","score":0.8679999709129333},{"id":"https://openalex.org/keywords/complex-networks","display_name":"complex networks","score":0.5979999899864197},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.8849999904632568}],"concepts":[{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.7803428769111633},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.7684717774391174},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7674732208251953},{"id":"https://openalex.org/C97172818","wikidata":"https://www.wikidata.org/wiki/Q7520904","display_name":"Simplicial manifold","level":5,"score":0.6289325952529907},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.554915189743042},{"id":"https://openalex.org/C3469331","wikidata":"https://www.wikidata.org/wiki/Q7520902","display_name":"Simplicial homology","level":3,"score":0.547200620174408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5372772812843323},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.5363012552261353},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.5349387526512146},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46131017804145813},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.43958595395088196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.425289124250412},{"id":"https://openalex.org/C127634017","wikidata":"https://www.wikidata.org/wiki/Q5627866","display_name":"h-vector","level":3,"score":0.4227873980998993},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.41161221265792847},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36117202043533325},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34618765115737915},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3095923662185669},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25577837228775024},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.1564139425754547},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06752794981002808},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2964728636","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.02583","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2964728636","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.02583","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1496383623","https://openalex.org/W1915374658","https://openalex.org/W2002243081","https://openalex.org/W2002532150","https://openalex.org/W2025796118","https://openalex.org/W2071391326","https://openalex.org/W2097308346","https://openalex.org/W2124637492","https://openalex.org/W2126424784","https://openalex.org/W2131760256","https://openalex.org/W2134703872","https://openalex.org/W2135610119","https://openalex.org/W2223193774","https://openalex.org/W2424211690","https://openalex.org/W2748936567","https://openalex.org/W2767674461","https://openalex.org/W2787887656","https://openalex.org/W2807785447","https://openalex.org/W2941564413","https://openalex.org/W2962849396","https://openalex.org/W2964171580","https://openalex.org/W2970791029"],"related_works":["https://openalex.org/W3024772221","https://openalex.org/W2965518725","https://openalex.org/W3016951513","https://openalex.org/W3195683952","https://openalex.org/W4386584721","https://openalex.org/W4408977830","https://openalex.org/W3192120168","https://openalex.org/W2134703872","https://openalex.org/W2060850351","https://openalex.org/W4200571376"],"abstract_inverted_index":{"Many":[0],"real":[1],"networks":[2],"in":[3,42,49,62,88,106,126,200],"social,":[4],"biological":[5],"or":[6],"computer":[7],"sciences":[8],"have":[9],"an":[10,40,127,153,177],"inherent":[11],"structure":[12],"of":[13,26,32,39,45,51,54,70,95,176,180,183,195],"a":[14,43,63,107,135,181,186,201],"simplicial":[15,64,108,129,187,202,217],"complex,":[16,109],"which":[17],"reflects":[18],"the":[19,30,37,52,145,158,172,193],"multi":[20,120,137],"interactions":[21],"among":[22,114],"agents":[23],"(and":[24],"groups":[25],"agents)":[27],"and":[28,61,72,100,116,123,134,148,189,209],"constitutes":[29],"basics":[31],"Topological":[33],"Data":[34],"Analysis.":[35],"Normally,":[36],"relevance":[38,173],"agent":[41],"network":[44,65],"graphs":[46],"is":[47,140],"given":[48,133],"terms":[50],"number":[53],"edges":[55],"incident":[56],"to":[57,151,170,191,216],"it,":[58],"its":[59],"degree,":[60],"there":[66],"are":[67,82,131,149,207,220],"already":[68],"notions":[69,94],"adjacency":[71,102],"degree":[73,194],"for":[74,85,104,156],"simplices":[75,87,105],"that,":[76],"as":[77,79,185],"far":[78],"we":[80],"know,":[81],"not":[83,174],"valid":[84],"comparing":[86],"different":[89,198],"dimensions.":[90],"We":[91],"propose":[92],"new":[93],"higher":[96,159],"order":[97,160],"lower,":[98],"upper":[99],"generalised":[101],"degrees":[103,161],"allowing":[110],"any":[111],"dimensional":[112],"comparison":[113],"them":[115,184],"their":[117],"faces.":[118],"New":[119],"parameter":[121],"boundary":[122],"coboundary":[124],"operators":[125,143],"oriented":[128],"complex":[130],"also":[132,190,221],"novel":[136],"combinatorial":[138],"Laplacian":[139],"defined.":[141],"These":[142],"generalise":[144],"known":[146],"ones":[147],"proved":[150],"be":[152],"effective":[154,208],"tool":[155],"calculating":[157],"here":[162],"presented.":[163],"Thus,":[164],"this":[165],"mathematical":[166],"framework":[167],"allows":[168],"us":[169],"elucidate":[171],"only":[175],"agent,":[178],"but":[179],"bunch":[182],"community,":[188],"study":[192],"collaboration":[196],"between":[197],"communities":[199],"complex.":[203],"In":[204],"addition,":[205],"they":[206],"programmable":[210],"computational":[211],"techniques.":[212],"Some":[213],"potential":[214],"applications":[215],"Network":[218],"Science":[219],"proposed.":[222]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-08-13T00:00:00"}
