{"id":"https://openalex.org/W1844872857","doi":"https://doi.org/10.1109/tcsi.2012.2215780","title":"Kron Reduction of Graphs With Applications to Electrical Networks","display_name":"Kron Reduction of Graphs With Applications to Electrical Networks","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1844872857","doi":"https://doi.org/10.1109/tcsi.2012.2215780","mag":"1844872857"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2012.2215780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2215780","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1102.2950","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091434894","display_name":"Florian D\u00f6rfler","orcid":"https://orcid.org/0000-0002-9649-5305"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Florian Dorfler","raw_affiliation_strings":["Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, United States","Center for Control, Dynamical Syst. & Comput, Univ. of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, United States","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Center for Control, Dynamical Syst. & Comput, Univ. of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, United States","Center for Control, Dynamical Syst. & Comput, Univ. of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, United States","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Center for Control, Dynamical Syst. & Comput, Univ. of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091434894"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":1.6816,"has_fulltext":true,"cited_by_count":60,"citation_normalized_percentile":{"value":0.84963526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"60","issue":"1","first_page":"150","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10083","display_name":"Graphene research and applications","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962999820709229,"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/laplacian-matrix","display_name":"Laplacian matrix","score":0.7008408308029175},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.5274308323860168},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5213322043418884},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4997413158416748},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.49531832337379456},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4737620949745178},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4713798463344574},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4586150646209717},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43604737520217896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3835064768791199},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3794096112251282},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.37899067997932434},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3585008978843689},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10452908277511597}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.7008408308029175},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.5274308323860168},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5213322043418884},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4997413158416748},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.49531832337379456},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4737620949745178},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4713798463344574},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4586150646209717},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43604737520217896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3835064768791199},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3794096112251282},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37899067997932434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3585008978843689},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10452908277511597},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tcsi.2012.2215780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2215780","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1102.2950","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1102.2950","pdf_url":"https://arxiv.org/pdf/1102.2950","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":"mag:1844872857","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1102.2950","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1102.2950","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1102.2950","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:arXiv.org:1102.2950","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1102.2950","pdf_url":"https://arxiv.org/pdf/1102.2950","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6183229268","display_name":"Collaborative Research:   CSR-EHCS(EHS), TM:   Distributed Sensing via Robust Consensus on Manifolds","funder_award_id":"0834446","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7332492814","display_name":"RI: Medium: Collaborative Research: Minimalist Mapping and Monitoring","funder_award_id":"0904501","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7926871209","display_name":null,"funder_award_id":"CNS-0834446","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1844872857.pdf","grobid_xml":"https://content.openalex.org/works/W1844872857.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W51449675","https://openalex.org/W60687185","https://openalex.org/W68634354","https://openalex.org/W247697463","https://openalex.org/W261461018","https://openalex.org/W391578156","https://openalex.org/W585033315","https://openalex.org/W1498989325","https://openalex.org/W1503728220","https://openalex.org/W1506342804","https://openalex.org/W1521492382","https://openalex.org/W1524826225","https://openalex.org/W1542938076","https://openalex.org/W1595379210","https://openalex.org/W1606815384","https://openalex.org/W1612171427","https://openalex.org/W1969517930","https://openalex.org/W1969823477","https://openalex.org/W1980119950","https://openalex.org/W1983224659","https://openalex.org/W1983677661","https://openalex.org/W1988420772","https://openalex.org/W1995051706","https://openalex.org/W1999683177","https://openalex.org/W2000106105","https://openalex.org/W2009561564","https://openalex.org/W2017587938","https://openalex.org/W2023998244","https://openalex.org/W2039442257","https://openalex.org/W2040165403","https://openalex.org/W2042534939","https://openalex.org/W2042624802","https://openalex.org/W2043883312","https://openalex.org/W2049732772","https://openalex.org/W2050351695","https://openalex.org/W2054078412","https://openalex.org/W2054897957","https://openalex.org/W2058492355","https://openalex.org/W2076596987","https://openalex.org/W2076736217","https://openalex.org/W2077350444","https://openalex.org/W2085170137","https://openalex.org/W2098210428","https://openalex.org/W2102958772","https://openalex.org/W2104849640","https://openalex.org/W2110518840","https://openalex.org/W2118469889","https://openalex.org/W2121819629","https://openalex.org/W2122605444","https://openalex.org/W2132850926","https://openalex.org/W2149298047","https://openalex.org/W2151386472","https://openalex.org/W2151891567","https://openalex.org/W2161984370","https://openalex.org/W2167064216","https://openalex.org/W2610857016","https://openalex.org/W2964350268","https://openalex.org/W4254980318","https://openalex.org/W6602489041","https://openalex.org/W6668598528"],"related_works":["https://openalex.org/W2525986745","https://openalex.org/W2396107515","https://openalex.org/W55190912","https://openalex.org/W3000288649","https://openalex.org/W3115014921","https://openalex.org/W1537447662","https://openalex.org/W2169811919","https://openalex.org/W2152511758","https://openalex.org/W3128752551","https://openalex.org/W3103352262","https://openalex.org/W2904592667","https://openalex.org/W2153492814","https://openalex.org/W2963887197","https://openalex.org/W3098240653","https://openalex.org/W3098951945","https://openalex.org/W3139567713","https://openalex.org/W2735636386","https://openalex.org/W2217030094","https://openalex.org/W2122450469","https://openalex.org/W2021812446"],"abstract_inverted_index":{"Consider":[0],"a":[1,27,46,135],"weighted":[2],"undirected":[3],"graph":[4,24,28,130],"and":[5,61,76,93,137,149,173,189],"its":[6],"corresponding":[7,16],"Laplacian":[8,30,41],"matrix,":[9],"possibly":[10],"augmented":[11],"with":[12,43],"additional":[13],"diagonal":[14],"elements":[15],"to":[17,45,165,182],"self-loops.":[18],"The":[19,51],"Kron":[20,52,81,122,142,179],"reduction":[21,53,82,96,123,143,180],"of":[22,38,49,78,97,128,141,162,178],"this":[23,117],"is":[25,32,55,83],"again":[26],"whose":[29],"matrix":[31,42],"obtained":[33],"by":[34],"the":[35,39,95,111,121,126,159,187,190],"Schur":[36],"complement":[37],"original":[40],"respect":[44],"specified":[47],"subset":[48],"nodes.":[50],"process":[54,124],"ubiquitous":[56],"in":[57,62,86,90,94,110,170],"classic":[58],"circuit":[59],"theory":[60],"related":[63],"disciplines":[64],"such":[65],"as":[66,106],"electrical":[67],"impedance":[68],"tomography,":[69],"smart":[70],"grid":[71],"monitoring,":[72],"transient":[73],"stability":[74],"assessment,":[75],"analysis":[77,140,177],"power":[79],"electronics.":[80],"also":[84,103],"relevant":[85],"other":[87],"physical":[88,191],"domains,":[89],"computational":[91],"applications,":[92],"Markov":[98],"chains.":[99],"Related":[100],"concepts":[101],"have":[102],"been":[104],"studied":[105],"purely":[107],"theoretic":[108,154],"problems":[109],"literature":[112],"on":[113,186],"linear":[114,174],"algebra.":[115,175],"In":[116],"paper":[118],"we":[119,133,156],"analyze":[120],"from":[125],"viewpoint":[127],"algebraic":[129],"theory.":[131],"Specifically,":[132],"provide":[134],"comprehensive":[136],"detailed":[138],"graph-theoretic":[139],"encompassing":[144],"topological,":[145],"algebraic,":[146],"spectral,":[147],"resistive,":[148],"sensitivity":[150],"analyses.":[151],"Throughout":[152],"our":[153,163],"elaborations":[155],"especially":[157],"emphasize":[158],"practical":[160],"applicability":[161],"results":[164],"various":[166],"problem":[167],"setups":[168],"arising":[169],"engineering,":[171],"computation,":[172],"Our":[176],"leads":[181],"novel":[183],"insights":[184],"both":[185],"mathematical":[188],"side.":[192]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}