{"id":"https://openalex.org/W2969075317","doi":"https://doi.org/10.1093/comnet/cnz030","title":"The structural properties and the spanning trees entropy of the generalized Fractal Scale-Free Lattice","display_name":"The structural properties and the spanning trees entropy of the generalized Fractal Scale-Free Lattice","publication_year":2019,"publication_date":"2019-07-16","ids":{"openalex":"https://openalex.org/W2969075317","doi":"https://doi.org/10.1093/comnet/cnz030","mag":"2969075317"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnz030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnz030","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043840859","display_name":"Raihana Mokhlissi","orcid":"https://orcid.org/0000-0001-8870-5838"},"institutions":[{"id":"https://openalex.org/I126477371","display_name":"Mohammed V University","ror":"https://ror.org/00r8w8f84","country_code":"MA","type":"education","lineage":["https://openalex.org/I126477371"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Raihana Mokhlissi","raw_affiliation_strings":["LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco"],"affiliations":[{"raw_affiliation_string":"LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco","institution_ids":["https://openalex.org/I126477371"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023182153","display_name":"Dounia Lotfi","orcid":"https://orcid.org/0009-0002-7995-4036"},"institutions":[{"id":"https://openalex.org/I126477371","display_name":"Mohammed V University","ror":"https://ror.org/00r8w8f84","country_code":"MA","type":"education","lineage":["https://openalex.org/I126477371"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Dounia Lotfi","raw_affiliation_strings":["LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco"],"affiliations":[{"raw_affiliation_string":"LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco","institution_ids":["https://openalex.org/I126477371"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110439926","display_name":"Mohamed El Marraki","orcid":null},"institutions":[{"id":"https://openalex.org/I126477371","display_name":"Mohammed V University","ror":"https://ror.org/00r8w8f84","country_code":"MA","type":"education","lineage":["https://openalex.org/I126477371"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohamed El Marraki","raw_affiliation_strings":["LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco"],"affiliations":[{"raw_affiliation_string":"LRIT\u2014CNRST URAC 29, Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, B.P 1014 Rabat, Morocco","institution_ids":["https://openalex.org/I126477371"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108350545","display_name":"Joyati Debnath","orcid":null},"institutions":[{"id":"https://openalex.org/I5795714","display_name":"Winona State University","ror":"https://ror.org/00kmxt141","country_code":"US","type":"education","lineage":["https://openalex.org/I5795714","https://openalex.org/I91221267"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joyati Debnath","raw_affiliation_strings":["Winona State University, Winona, MN 55987, USA"],"affiliations":[{"raw_affiliation_string":"Winona State University, Winona, MN 55987, USA","institution_ids":["https://openalex.org/I5795714"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043840859"],"corresponding_institution_ids":["https://openalex.org/I126477371"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.1448,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.45371665,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"2","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":0.9961000084877014,"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":0.9961000084877014,"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":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.963100016117096,"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/fractal","display_name":"Fractal","score":0.7051901817321777},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.6475063562393188},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5871284008026123},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5142986178398132},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4780426621437073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45410048961639404},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.44167137145996094},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4404720962047577},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.43194031715393066},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.4314255714416504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3783162236213684},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3100205957889557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1538097858428955},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12747344374656677}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7051901817321777},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.6475063562393188},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5871284008026123},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5142986178398132},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4780426621437073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45410048961639404},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.44167137145996094},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4404720962047577},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.43194031715393066},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.4314255714416504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3783162236213684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3100205957889557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1538097858428955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12747344374656677},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comnet/cnz030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnz030","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5099999904632568,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G5604347370","display_name":null,"funder_award_id":"43UM5R2015","funder_id":"https://openalex.org/F4320323771","funder_display_name":"Centre National pour la Recherche Scientifique et Technique"}],"funders":[{"id":"https://openalex.org/F4320323771","display_name":"Centre National pour la Recherche Scientifique et Technique","ror":"https://ror.org/00675rp98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W606008011","https://openalex.org/W637910104","https://openalex.org/W647522939","https://openalex.org/W1484040084","https://openalex.org/W1555893171","https://openalex.org/W1620417316","https://openalex.org/W1807017871","https://openalex.org/W1932416503","https://openalex.org/W1965922183","https://openalex.org/W1978493550","https://openalex.org/W1983380661","https://openalex.org/W1997371824","https://openalex.org/W1998741088","https://openalex.org/W2003073299","https://openalex.org/W2008620264","https://openalex.org/W2013872122","https://openalex.org/W2018778266","https://openalex.org/W2019789576","https://openalex.org/W2020125634","https://openalex.org/W2037685751","https://openalex.org/W2051781104","https://openalex.org/W2058162908","https://openalex.org/W2061309095","https://openalex.org/W2068861748","https://openalex.org/W2069401760","https://openalex.org/W2078584887","https://openalex.org/W2090296229","https://openalex.org/W2092153036","https://openalex.org/W2103475700","https://openalex.org/W2112090702","https://openalex.org/W2118009636","https://openalex.org/W2121699196","https://openalex.org/W2129025140","https://openalex.org/W2130790725","https://openalex.org/W2148246509","https://openalex.org/W2160058983","https://openalex.org/W2179119116","https://openalex.org/W2284114063","https://openalex.org/W2503654778","https://openalex.org/W2569576787","https://openalex.org/W2613824014","https://openalex.org/W2616697817","https://openalex.org/W2624277423","https://openalex.org/W2749722112","https://openalex.org/W2757195549","https://openalex.org/W2797443475","https://openalex.org/W2889374003","https://openalex.org/W3102587357","https://openalex.org/W3103828585","https://openalex.org/W3108965212","https://openalex.org/W4237169760","https://openalex.org/W4302604684","https://openalex.org/W4312512934","https://openalex.org/W4386628099","https://openalex.org/W6636435543","https://openalex.org/W6669064855","https://openalex.org/W6685675689","https://openalex.org/W6695953332","https://openalex.org/W6730551316","https://openalex.org/W6738002306","https://openalex.org/W6739439112"],"related_works":["https://openalex.org/W2099915933","https://openalex.org/W2418231958","https://openalex.org/W4380840098","https://openalex.org/W3116169590","https://openalex.org/W2394117909","https://openalex.org/W1703428550","https://openalex.org/W2044443696","https://openalex.org/W2896054214","https://openalex.org/W3101281637","https://openalex.org/W2355197944"],"abstract_inverted_index":{"Abstract":[0],"Enumerating":[1],"all":[2],"the":[3,28,49,55,62,68,74,84,87,101],"spanning":[4,71],"trees":[5,72],"of":[6,27,70,86],"a":[7,25,43],"complex":[8,98],"network":[9],"is":[10],"theoretical":[11],"defiance":[12],"for":[13],"mathematicians,":[14],"electrical":[15],"engineers":[16],"and":[17,32,92],"computer":[18],"scientists.":[19],"In":[20,58],"this":[21],"article,":[22],"we":[23,33,46,60,90],"propose":[24],"generalization":[26,51],"Fractal":[29,76],"Scale-Free":[30,77],"Lattice":[31],"study":[34],"its":[35,39,94],"structural":[36],"properties.":[37],"As":[38],"degree":[40],"distribution":[41],"follows":[42],"power":[44],"law,":[45],"prove":[47],"that":[48],"proposed":[50],"does":[52],"not":[53],"affect":[54],"scale-free":[56],"property.":[57],"addition,":[59],"use":[61],"electrically":[63],"equivalent":[64],"transformations":[65],"to":[66,82],"count":[67],"number":[69],"in":[73,80],"generalized":[75,88],"Lattice.":[78],"Finally,":[79],"order":[81],"evaluate":[83],"robustness":[85],"lattice,":[89],"compute":[91],"compare":[93],"entropy":[95],"with":[96],"other":[97],"networks":[99],"having":[100],"same":[102],"average":[103],"degree.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}