{"id":"https://openalex.org/W2766738887","doi":"https://doi.org/10.1109/rndm.2017.8093019","title":"Variations in graph energy: A measure for network resilience","display_name":"Variations in graph energy: A measure for network resilience","publication_year":2017,"publication_date":"2017-09-01","ids":{"openalex":"https://openalex.org/W2766738887","doi":"https://doi.org/10.1109/rndm.2017.8093019","mag":"2766738887"},"language":"en","primary_location":{"id":"doi:10.1109/rndm.2017.8093019","is_oa":false,"landing_page_url":"https://doi.org/10.1109/rndm.2017.8093019","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 9th International Workshop on Resilient Networks Design and Modeling (RNDM)","raw_type":"proceedings-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/A5024096832","display_name":"Tristan A. Shatto","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tristan A. Shatto","raw_affiliation_strings":["Department of Electrical and Computer Engineering"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058060546","display_name":"Egemen K. \u00c7etinkaya","orcid":"https://orcid.org/0000-0002-6394-4565"},"institutions":[{"id":"https://openalex.org/I20382870","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12","country_code":"US","type":"education","lineage":["https://openalex.org/I20382870"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Egemen K. Cetinkaya","raw_affiliation_strings":["Department of Electrical and Computer Engineering","Intelligent Systems Center, Missouri University of Science and Technology, Rolla, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering","institution_ids":[]},{"raw_affiliation_string":"Intelligent Systems Center, Missouri University of Science and Technology, Rolla, MO, USA","institution_ids":["https://openalex.org/I20382870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024096832"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5161,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.64742134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9983999729156494,"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":0.9983999729156494,"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/T11476","display_name":"Graph theory and applications","score":0.998199999332428,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9056000113487244,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.7485688328742981},{"id":"https://openalex.org/keywords/graph-energy","display_name":"Graph energy","score":0.6137118935585022},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6127333641052246},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6085352301597595},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5090024471282959},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4982492923736572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4802544414997101},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4617398679256439},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.4612824320793152},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42484304308891296},{"id":"https://openalex.org/keywords/regular-graph","display_name":"Regular graph","score":0.42167648673057556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38259437680244446},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30167877674102783},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.29956525564193726},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.28614336252212524},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1733367145061493},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10564503073692322},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07507526874542236}],"concepts":[{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7485688328742981},{"id":"https://openalex.org/C78913703","wikidata":"https://www.wikidata.org/wiki/Q5597087","display_name":"Graph energy","level":5,"score":0.6137118935585022},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6127333641052246},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6085352301597595},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5090024471282959},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4982492923736572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4802544414997101},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4617398679256439},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.4612824320793152},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42484304308891296},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.42167648673057556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38259437680244446},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30167877674102783},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.29956525564193726},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.28614336252212524},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1733367145061493},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10564503073692322},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07507526874542236}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/rndm.2017.8093019","is_oa":false,"landing_page_url":"https://doi.org/10.1109/rndm.2017.8093019","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 9th International Workshop on Resilient Networks Design and Modeling (RNDM)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8299999833106995}],"awards":[],"funders":[{"id":"https://openalex.org/F4320312855","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1499220558","https://openalex.org/W1578099820","https://openalex.org/W1587744656","https://openalex.org/W1593155847","https://openalex.org/W1980156780","https://openalex.org/W1992694598","https://openalex.org/W1998603792","https://openalex.org/W2002653466","https://openalex.org/W2011301426","https://openalex.org/W2021356981","https://openalex.org/W2029173860","https://openalex.org/W2056944867","https://openalex.org/W2088216145","https://openalex.org/W2099168712","https://openalex.org/W2131006316","https://openalex.org/W2131467982","https://openalex.org/W2132022337","https://openalex.org/W2137496495","https://openalex.org/W2146292423","https://openalex.org/W2146607065","https://openalex.org/W2153988305","https://openalex.org/W2167970280","https://openalex.org/W2960157754","https://openalex.org/W4230572909","https://openalex.org/W6679576325","https://openalex.org/W6765555641"],"related_works":["https://openalex.org/W2165755074","https://openalex.org/W2782821035","https://openalex.org/W1547104907","https://openalex.org/W2575552581","https://openalex.org/W2389330739","https://openalex.org/W2963150133","https://openalex.org/W2549624392","https://openalex.org/W4254484011","https://openalex.org/W4293849741","https://openalex.org/W4318995835"],"abstract_inverted_index":{"There":[0],"are":[1,14,26],"many":[2],"models":[3],"and":[4,25,58,90,102,108,115,150],"metrics":[5],"developed":[6],"to":[7,30,71,127,132],"study":[8],"the":[9,15,18,42,55,87,118,133,145],"resilience":[10,81],"of":[11,17,44,47,83,139,148],"networks.":[12],"Eigenvalues":[13],"roots":[16],"characteristic":[19],"polynomial":[20],"for":[21],"a":[22,31,51,79,128],"given":[23],"graph":[24,39,61,75,93,110],"mathematically":[27],"rigorous":[28],"compared":[29],"statistical":[32],"measure":[33],"such":[34],"as":[35],"degree":[36],"distribution.":[37],"The":[38,136],"energy":[40,62,76,111,121],"is":[41,50,70,142],"sum":[43],"absolute":[45],"values":[46,147],"eigenvalues;":[48],"there":[49],"subtle":[52],"difference":[53],"between":[54],"adjacency,":[56,88],"Laplacian,":[57,89],"normalized":[59,91,119],"Laplacian":[60,92,109,120,151],"calculations.":[63],"Our":[64],"primary":[65],"objective":[66],"in":[67],"this":[68],"paper":[69],"understand":[72],"what":[73],"different":[74],"mean":[77],"from":[78],"network":[80,134],"point":[82],"view.":[84],"We":[85],"calculate":[86],"energies":[94],"on":[95],"four":[96],"backbone":[97],"networks":[98],"under":[99],"targeted":[100],"node":[101,114],"link":[103,116,124],"attack":[104],"scenarios.":[105],"While":[106],"adjacency":[107,149],"decrease":[112],"with":[113,123],"attacks,":[117],"increases":[122],"attacks":[125],"converging":[126],"maximum":[129],"value":[130],"equal":[131],"order.":[135],"structural":[137],"similarities":[138],"physical-level":[140],"topologies":[141],"revealed":[143],"by":[144],"close":[146],"energies.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}