{"id":"https://openalex.org/W2270734194","doi":"https://doi.org/10.1093/comnet/cnw005","title":"Planar growth generates scale-free networks","display_name":"Planar growth generates scale-free networks","publication_year":2016,"publication_date":"2016-03-14","ids":{"openalex":"https://openalex.org/W2270734194","doi":"https://doi.org/10.1093/comnet/cnw005","mag":"2270734194"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnw005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnw005","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/14dc267e-0c81-4773-9080-e755d6e4155f","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002586235","display_name":"Garvin Haslett","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Garvin Haslett","raw_affiliation_strings":["Institute for Complex Systems Simulation, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Institute for Complex Systems Simulation, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052396839","display_name":"Seth Bullock","orcid":"https://orcid.org/0000-0003-4371-5965"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Seth Bullock","raw_affiliation_strings":["Department of Computer Science, University of Bristol, Bristol BS8 1UB, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bristol, Bristol BS8 1UB, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000066138","display_name":"Markus Brede","orcid":"https://orcid.org/0000-0002-0197-8612"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Markus Brede","raw_affiliation_strings":["Institute for Complex Systems Simulation, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Institute for Complex Systems Simulation, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002586235"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01135424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"cnw005","last_page":"cnw005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9750999808311462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.8392561674118042},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.7108176946640015},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.684701681137085},{"id":"https://openalex.org/keywords/crossover","display_name":"Crossover","score":0.6202496886253357},{"id":"https://openalex.org/keywords/scale-free-network","display_name":"Scale-free network","score":0.6090505719184875},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.5953448414802551},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.5279302597045898},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.5212001204490662},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.512673020362854},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.44662246108055115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4438605308532715},{"id":"https://openalex.org/keywords/hierarchical-network-model","display_name":"Hierarchical network model","score":0.43461689352989197},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.4327344298362732},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.42395147681236267},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40451663732528687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4022834300994873},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2984580397605896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2895664870738983},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13276135921478271},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09963613748550415},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09309205412864685}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.8392561674118042},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.7108176946640015},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.684701681137085},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.6202496886253357},{"id":"https://openalex.org/C25580894","wikidata":"https://www.wikidata.org/wiki/Q1071058","display_name":"Scale-free network","level":3,"score":0.6090505719184875},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.5953448414802551},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.5279302597045898},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.5212001204490662},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.512673020362854},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.44662246108055115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4438605308532715},{"id":"https://openalex.org/C64900535","wikidata":"https://www.wikidata.org/wiki/Q5753111","display_name":"Hierarchical network model","level":3,"score":0.43461689352989197},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.4327344298362732},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.42395147681236267},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40451663732528687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4022834300994873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2984580397605896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2895664870738983},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13276135921478271},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09963613748550415},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09309205412864685},{"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1093/comnet/cnw005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnw005","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"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/14dc267e-0c81-4773-9080-e755d6e4155f","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/14dc267e-0c81-4773-9080-e755d6e4155f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Haslett, G, Bullock, S & Brede, M 2016, 'Planar growth generates scale-free networks', Journal of Complex Networks, vol. 4, no. 4, pp. 500-516. https://doi.org/10.1093/comnet/cnw005","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.soton.ac.uk:388773","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1602.03774","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.03774","pdf_url":"https://arxiv.org/pdf/1602.03774","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/14dc267e-0c81-4773-9080-e755d6e4155f","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/14dc267e-0c81-4773-9080-e755d6e4155f","pdf_url":"https://research-information.bris.ac.uk/ws/files/72372452/complexnets2016.pdf","source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Haslett, G, Bullock, S & Brede, M 2016, 'Planar growth generates scale-free networks', Journal of Complex Networks, vol. 4, no. 4, pp. 500-516. https://doi.org/10.1093/comnet/cnw005","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1602.03774","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.03774","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire/14dc267e-0c81-4773-9080-e755d6e4155f","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/14dc267e-0c81-4773-9080-e755d6e4155f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Haslett, G, Bullock, S & Brede, M 2016, 'Planar growth generates scale-free networks', Journal of Complex Networks, vol. 4, no. 4, pp. 500-516. https://doi.org/10.1093/comnet/cnw005","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1495430942","https://openalex.org/W1521235291","https://openalex.org/W1572272766","https://openalex.org/W1579767335","https://openalex.org/W1584977346","https://openalex.org/W1842343833","https://openalex.org/W1875112053","https://openalex.org/W1973012017","https://openalex.org/W1976668093","https://openalex.org/W1989742356","https://openalex.org/W1993324602","https://openalex.org/W1997193964","https://openalex.org/W1997741784","https://openalex.org/W1998071216","https://openalex.org/W2000042664","https://openalex.org/W2008620264","https://openalex.org/W2008874832","https://openalex.org/W2009104529","https://openalex.org/W2014173443","https://openalex.org/W2030249432","https://openalex.org/W2032831962","https://openalex.org/W2039805904","https://openalex.org/W2039964641","https://openalex.org/W2040956707","https://openalex.org/W2045824643","https://openalex.org/W2047968474","https://openalex.org/W2050102166","https://openalex.org/W2053015976","https://openalex.org/W2059161157","https://openalex.org/W2063539292","https://openalex.org/W2067679320","https://openalex.org/W2072059712","https://openalex.org/W2075523351","https://openalex.org/W2076222538","https://openalex.org/W2079942817","https://openalex.org/W2081245596","https://openalex.org/W2088856850","https://openalex.org/W2089516597","https://openalex.org/W2092184130","https://openalex.org/W2094247852","https://openalex.org/W2098674006","https://openalex.org/W2103510045","https://openalex.org/W2105510821","https://openalex.org/W2106180925","https://openalex.org/W2112090702","https://openalex.org/W2119004437","https://openalex.org/W2120698442","https://openalex.org/W2121821841","https://openalex.org/W2123386188","https://openalex.org/W2135641060","https://openalex.org/W2140488329","https://openalex.org/W2148606196","https://openalex.org/W2149141576","https://openalex.org/W2152058154","https://openalex.org/W2165211369","https://openalex.org/W2168632251","https://openalex.org/W2950005757","https://openalex.org/W3037085755","https://openalex.org/W3103362336","https://openalex.org/W3106480620","https://openalex.org/W3122027017","https://openalex.org/W3124579699","https://openalex.org/W4238452917","https://openalex.org/W4250386952","https://openalex.org/W4295953407","https://openalex.org/W6678569463"],"related_works":["https://openalex.org/W2964304336","https://openalex.org/W2281204610","https://openalex.org/W2130919150","https://openalex.org/W3124021083","https://openalex.org/W1960772788","https://openalex.org/W3104609558","https://openalex.org/W1864446665","https://openalex.org/W2092157184","https://openalex.org/W3157647423","https://openalex.org/W2895693697","https://openalex.org/W1961558643","https://openalex.org/W1503879265","https://openalex.org/W2611952155","https://openalex.org/W2953111892","https://openalex.org/W2065118416","https://openalex.org/W1808535251","https://openalex.org/W1666854045","https://openalex.org/W2131529378","https://openalex.org/W2765427013","https://openalex.org/W3139529257"],"abstract_inverted_index":{"In":[0],"this":[1,151],"paper,":[2],"we":[3],"introduce":[4],"a":[5,21,46,64,89,98,121,140],"model":[6,84,119],"of":[7,66,71,91,102],"spatial":[8],"network":[9,44,73],"growth":[10,76,94],"in":[11,24],"which":[12],"nodes":[13,32],"are":[14,63],"placed":[15],"at":[16],"randomly":[17],"selected":[18],"locations":[19],"on":[20],"unit":[22],"square":[23],"|$\\mathbb":[25],"{R}^2$|\u2060,":[26],"forming":[27],"new":[28],"connections":[29],"to":[30,34,146],"old":[31],"subject":[33],"the":[35,54,67,72,83,105,110,128],"constraint":[36,130],"that":[37,60,82],"edges":[38],"do":[39],"not":[40],"cross.":[41],"The":[42],"resulting":[43],"has":[45],"power":[47,144],"law":[48,145],"degree":[49,148],"distribution,":[50],"high":[51],"clustering":[52],"and":[53,77,95,109,117,138],"small":[55],"world":[56],"property.":[57],"We":[58,80,125],"argue":[59],"these":[61],"characteristics":[62],"consequence":[65],"two":[68],"defining":[69],"features":[70],"formation":[74],"procedure;":[75],"planarity":[78,129],"conservation.":[79],"demonstrate":[81],"can":[85],"be":[86],"understood":[87],"as":[88,114,120],"variant":[90],"random":[92],"Apollonian":[93,107,112],"further":[96],"propose":[97],"one":[99],"parameter":[100],"family":[101],"models":[103],"with":[104,135],"Random":[106],"Network":[108,113],"Deterministic":[111],"extreme":[115],"cases":[116],"our":[118],"midpoint":[122],"between":[123],"them.":[124],"then":[126],"relax":[127],"by":[131],"allowing":[132],"edge":[133],"crossings":[134],"some":[136],"probability":[137,152],"find":[139],"smooth":[141],"crossover":[142],"from":[143],"exponential":[147],"distributions":[149],"when":[150],"is":[153],"increased.":[154]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}