{"id":"https://openalex.org/W4237486254","doi":"https://doi.org/10.1002/net.3230130303","title":"Conditional connectivity","display_name":"Conditional connectivity","publication_year":1983,"publication_date":"1983-09-01","ids":{"openalex":"https://openalex.org/W4237486254","doi":"https://doi.org/10.1002/net.3230130303"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230130303","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230130303","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5111801246","display_name":"Frank Harary","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Frank Harary","raw_affiliation_strings":["The University of Michigan, Ann Arbor, Michigan, Ml 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Michigan, Ann Arbor, Michigan, Ml 48109","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111801246"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":1.1426,"has_fulltext":false,"cited_by_count":426,"citation_normalized_percentile":{"value":0.80895645,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"13","issue":"3","first_page":"347","last_page":"357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9976999759674072,"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/combinatorics","display_name":"Combinatorics","score":0.5970516204833984},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5869663953781128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5556787252426147},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.542262077331543},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.5086077451705933},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.48890867829322815},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4765763282775879},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45149844884872437},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.44645512104034424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4456143379211426},{"id":"https://openalex.org/keywords/analogy","display_name":"Analogy","score":0.41170644760131836},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4046551585197449},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.13760477304458618}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5970516204833984},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5869663953781128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5556787252426147},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.542262077331543},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.5086077451705933},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.48890867829322815},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4765763282775879},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45149844884872437},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.44645512104034424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4456143379211426},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.41170644760131836},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4046551585197449},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.13760477304458618},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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:10.1002/net.3230130303","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230130303","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W83066922","https://openalex.org/W197939587","https://openalex.org/W925204230","https://openalex.org/W976211528","https://openalex.org/W1583617948","https://openalex.org/W1965211543","https://openalex.org/W1985061810","https://openalex.org/W1987920422","https://openalex.org/W1990574549","https://openalex.org/W2031245498","https://openalex.org/W2038129817","https://openalex.org/W2043507362","https://openalex.org/W2054220856","https://openalex.org/W2063292248","https://openalex.org/W2085948787","https://openalex.org/W2086429387","https://openalex.org/W2086605603","https://openalex.org/W2087952350","https://openalex.org/W2104668651","https://openalex.org/W2104968017","https://openalex.org/W2106603498","https://openalex.org/W2111510304","https://openalex.org/W2111912021","https://openalex.org/W2116418681","https://openalex.org/W2125993726","https://openalex.org/W2533637837","https://openalex.org/W2615060900","https://openalex.org/W2797378967","https://openalex.org/W4205898702","https://openalex.org/W4210731599","https://openalex.org/W4213060883","https://openalex.org/W4213214460","https://openalex.org/W4231597948","https://openalex.org/W4235728477","https://openalex.org/W4244424643","https://openalex.org/W4251146767","https://openalex.org/W6607996271","https://openalex.org/W6635028284","https://openalex.org/W6676655793","https://openalex.org/W6677501579"],"related_works":["https://openalex.org/W4322767636","https://openalex.org/W3019714789","https://openalex.org/W4379118151","https://openalex.org/W1984251932","https://openalex.org/W2014594560","https://openalex.org/W2143340273","https://openalex.org/W938372727","https://openalex.org/W4390189596","https://openalex.org/W4230093114","https://openalex.org/W2039866832"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"a":[2,23,51],"noncomplete":[3],"graph":[4,67],"G":[5,38,68],",":[6],"the":[7,14,47,65],"traditional":[8],"definition":[9],"of":[10,17,37,50,54,64,76],"its":[11],"connectivity":[12,36,95],"is":[13,46,80],"minimum":[15],"number":[16],"points":[18],"whose":[19],"removal":[20],"results":[21,93],"in":[22,89],"disconnected":[24,66],"subgraph":[25],"with":[26,39,91],"components":[27],"H":[28,31,62],"1":[29],",\u2026,":[30],"k":[32],".":[33],"The":[34],"conditional":[35],"respect":[40],"to":[41],"some":[42],"graph\u2010theoretic":[43],"property":[44,72],"P":[45,79,85],"smallest":[48],"cardinality":[49],"set":[52],"S":[53,70],"points,":[55],"if":[56],"any,":[57],"such":[58],"that":[59],"every":[60],"component":[61],"i":[63],"\u2010":[69],"has":[71],"P.":[73],"A":[74],"survey":[75],"promising":[77],"properties":[78],"presented.":[81],"Questions":[82],"for":[83],"various":[84],"\u2010connectivities":[86],"are":[87],"listed":[88],"analogy":[90],"known":[92],"on":[94],"and":[96],"line\u2010connectivity.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":37},{"year":2024,"cited_by_count":39},{"year":2023,"cited_by_count":44},{"year":2022,"cited_by_count":38},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":27},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":11}],"updated_date":"2026-05-15T08:27:34.491423","created_date":"2025-10-10T00:00:00"}