{"id":"https://openalex.org/W2032325318","doi":"https://doi.org/10.1002/net.3230110405","title":"Combinatorial properties of directed graphs useful in computing network reliability","display_name":"Combinatorial properties of directed graphs useful in computing network reliability","publication_year":1981,"publication_date":"1981-12-01","ids":{"openalex":"https://openalex.org/W2032325318","doi":"https://doi.org/10.1002/net.3230110405","mag":"2032325318"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230110405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230110405","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/A5043170226","display_name":"A. Satyanarayana","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Satyanarayana","raw_affiliation_strings":["Operations Research Center, University of California at Berkeley, Berkeley, California 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Operations Research Center, University of California at Berkeley, Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038186370","display_name":"Jane N. Hagstrom","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jane N. Hagstrom","raw_affiliation_strings":["Electronics Research Laboratory, University of California at Berkeley, Berkeley, California 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronics Research Laboratory, University of California at Berkeley, Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043170226"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":10.5836,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.98557197,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"4","first_page":"357","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9776999950408936,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.954200029373169,"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":0.7335431575775146},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.6023555994033813},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5631309151649475},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.5521447062492371},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5234445929527283},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5051570534706116},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48097217082977295},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.41527605056762695},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3757525682449341},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2715988755226135},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.10733893513679504}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7335431575775146},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.6023555994033813},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5631309151649475},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5521447062492371},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5234445929527283},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5051570534706116},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48097217082977295},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.41527605056762695},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3757525682449341},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2715988755226135},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.10733893513679504},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230110405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230110405","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":[{"id":"https://metadata.un.org/sdg/10","score":0.8399999737739563,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W2022535107","https://openalex.org/W2093645406","https://openalex.org/W2112967464","https://openalex.org/W2146354455"],"related_works":["https://openalex.org/W2789636091","https://openalex.org/W2282273380","https://openalex.org/W4296570398","https://openalex.org/W1498460077","https://openalex.org/W2076040942","https://openalex.org/W2113826940","https://openalex.org/W2367468405","https://openalex.org/W2952985052","https://openalex.org/W4300575715","https://openalex.org/W2288163449"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"is":[3,29,50],"concerned":[4],"with":[5,18,83],"the":[6,10,32,39,48,68,80,98,105],"problem":[7],"of":[8,35,47,56,67,79,100,104],"computing":[9],"probability":[11,36],"that":[12],"a":[13,23,63],"root":[14],"vertex":[15],"can":[16],"communicate":[17],"all":[19],"other":[20],"vertices":[21,103],"in":[22],"probabilistic":[24],"directed":[25],"graph.":[26],"One":[27],"method":[28],"to":[30,38,61,74,86],"apply":[31],"inclusion\u2010exclusion":[33,69],"principle":[34],"theory":[37],"event":[40],"\u201cat":[41],"least":[42],"one":[43],"rooted":[44],"spanning":[45,77],"tree":[46],"graph":[49],"working.\u201d":[51],"We":[52],"prove":[53],"combinatorial":[54],"properties":[55],"graphs":[57],"which":[58],"allow":[59],"us":[60],"derive":[62],"much":[64],"condensed":[65],"form":[66],"expression.":[70],"Each":[71],"term":[72],"corresponds":[73],"an":[75],"acyclic":[76],"subgraph":[78],"original":[81],"graph,":[82],"coefficient":[84],"equal":[85],"(\u22121)":[87],"b":[88,94],"\u2010":[89],"n":[90,96],"+1":[91],",":[92],"where":[93],"and":[95,102],"are":[97],"number":[99],"edges":[101],"subgraph,":[106],"respectively.":[107]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
