{"id":"https://openalex.org/W2934249881","doi":"https://doi.org/10.3390/sym11040452","title":"Isoperimetric Numbers of Randomly Perturbed Intersection Graphs","display_name":"Isoperimetric Numbers of Randomly Perturbed Intersection Graphs","publication_year":2019,"publication_date":"2019-04-01","ids":{"openalex":"https://openalex.org/W2934249881","doi":"https://doi.org/10.3390/sym11040452","mag":"2934249881"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040452","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040452","pdf_url":"https://www.mdpi.com/2073-8994/11/4/452/pdf?version=1554109742","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/4/452/pdf?version=1554109742","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079289428","display_name":"Yilun Shang","orcid":"https://orcid.org/0000-0002-2817-3400"},"institutions":[{"id":"https://openalex.org/I32394136","display_name":"Northumbria University","ror":"https://ror.org/049e6bc10","country_code":"GB","type":"education","lineage":["https://openalex.org/I32394136"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yilun Shang","raw_affiliation_strings":["Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK","institution_ids":["https://openalex.org/I32394136"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079289428"],"corresponding_institution_ids":["https://openalex.org/I32394136"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.288,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52712329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":95},"biblio":{"volume":"11","issue":"4","first_page":"452","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9957000017166138,"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":0.9749000072479248,"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/combinatorics","display_name":"Combinatorics","score":0.7590510845184326},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.7470054626464844},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.7247945666313171},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5766676664352417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5453722476959229},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.441457599401474},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.42154160141944885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4083431363105774},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38376376032829285},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2964777946472168}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7590510845184326},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.7470054626464844},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.7247945666313171},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5766676664352417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5453722476959229},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.441457599401474},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.42154160141944885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4083431363105774},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38376376032829285},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2964777946472168},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11040452","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040452","pdf_url":"https://www.mdpi.com/2073-8994/11/4/452/pdf?version=1554109742","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:nrl.northumbria.ac.uk:38672","is_oa":true,"landing_page_url":null,"pdf_url":"http://nrl.northumbria.ac.uk/id/eprint/38672/1/Shang%20-%20Isoperimetric%20Numbers%20of%20Randomly%20Perturbed%20Intersection%20Graphs%20OA.pdf","source":{"id":"https://openalex.org/S4306401884","display_name":"Northumbria Research Link (Northumbria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32394136","host_organization_name":"Northumbria University","host_organization_lineage":["https://openalex.org/I32394136"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:ceceb855d639408182103d67a8d4f7fb","is_oa":true,"landing_page_url":"https://doaj.org/article/ceceb855d639408182103d67a8d4f7fb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 452 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11040452","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040452","pdf_url":"https://www.mdpi.com/2073-8994/11/4/452/pdf?version=1554109742","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7400000095367432}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311737","display_name":"Northumbria University","ror":"https://ror.org/049e6bc10"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2934249881.pdf","grobid_xml":"https://content.openalex.org/works/W2934249881.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W581043525","https://openalex.org/W1214985307","https://openalex.org/W1467444581","https://openalex.org/W1637337126","https://openalex.org/W1875112053","https://openalex.org/W1973819999","https://openalex.org/W1982313773","https://openalex.org/W1982442837","https://openalex.org/W1993216347","https://openalex.org/W2006605460","https://openalex.org/W2018047324","https://openalex.org/W2027199101","https://openalex.org/W2057444879","https://openalex.org/W2064782937","https://openalex.org/W2079643325","https://openalex.org/W2108797586","https://openalex.org/W2110158710","https://openalex.org/W2112090702","https://openalex.org/W2114162748","https://openalex.org/W2116269350","https://openalex.org/W2125315567","https://openalex.org/W2151936673","https://openalex.org/W2165064763","https://openalex.org/W2170766502","https://openalex.org/W2219978534","https://openalex.org/W2336317531","https://openalex.org/W2508652287","https://openalex.org/W2585467485","https://openalex.org/W2901211293","https://openalex.org/W2953264933","https://openalex.org/W2962779128","https://openalex.org/W2963973919","https://openalex.org/W2964241396","https://openalex.org/W3000240341","https://openalex.org/W3100678396","https://openalex.org/W3104609322","https://openalex.org/W3106048825","https://openalex.org/W3124877770","https://openalex.org/W4234989302","https://openalex.org/W4236659380","https://openalex.org/W4238443289","https://openalex.org/W4247942259","https://openalex.org/W4250244821"],"related_works":["https://openalex.org/W2393012656","https://openalex.org/W4293733602","https://openalex.org/W2587882711","https://openalex.org/W4387415199","https://openalex.org/W4297156356","https://openalex.org/W2799900090","https://openalex.org/W2042006853","https://openalex.org/W4382491248","https://openalex.org/W2047527454","https://openalex.org/W2051035306"],"abstract_inverted_index":{"Social":[0],"networks":[1],"describe":[2],"social":[3,81],"interactions":[4],"between":[5],"people,":[6],"which":[7],"are":[8,61],"often":[9],"modeled":[10],"by":[11,26],"intersection":[12,20,56,111],"graphs.":[13],"In":[14],"this":[15],"paper,":[16],"we":[17,42],"propose":[18],"an":[19],"graph":[21,32,57],"model":[22],"that":[23,44,98],"is":[24,113],"induced":[25],"adding":[27],"a":[28,34],"sparse":[29],"random":[30],"bipartite":[31,36],"to":[33],"given":[35],"graph.":[37],"Under":[38],"some":[39],"mild":[40],"conditions,":[41],"show":[43],"the":[45,49,53,84,89,99,117,120],"vertex\u2013isoperimetric":[46],"number":[47,51],"and":[48,88],"edge\u2013isoperimetric":[50],"of":[52,101,116,119],"randomly":[54,109],"perturbed":[55,110],"on":[58,108],"n":[59,67],"vertices":[60],"\u03a9":[62],"(":[63],"1":[64],"/":[65],"ln":[66],")":[68],"asymptomatically":[69],"almost":[70],"surely.":[71],"Numerical":[72],"simulations":[73],"for":[74],"small":[75],"graphs":[76,112],"extracted":[77],"from":[78],"two":[79],"real-world":[80],"networks,":[82],"namely,":[83],"board":[85],"interlocking":[86],"network":[87],"scientific":[90],"collaboration":[91],"network,":[92],"were":[93],"performed.":[94],"It":[95],"was":[96],"revealed":[97],"effect":[100],"increasing":[102],"isoperimetric":[103],"numbers":[104],"(i.e.,":[105],"expansion":[106],"properties)":[107],"presumably":[114],"independent":[115],"order":[118],"network.":[121]},"counts_by_year":[{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}