{"id":"https://openalex.org/W2195033970","doi":"https://doi.org/10.1109/tnse.2017.2712064","title":"Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees","display_name":"Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees","publication_year":2017,"publication_date":"2017-06-06","ids":{"openalex":"https://openalex.org/W2195033970","doi":"https://doi.org/10.1109/tnse.2017.2712064","mag":"2195033970"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2017.2712064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2017.2712064","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","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/1512.03489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057261458","display_name":"V\u00edctor M. Preciado","orcid":"https://orcid.org/0000-0001-9998-8730"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor M. Preciado","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","[Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"[Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA]","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101965763","display_name":"M. Amin Rahimian","orcid":"https://orcid.org/0000-0001-9384-1041"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Amin Rahimian","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","[Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"[Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA]","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057261458"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":0.4858,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65956957,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"4","issue":"4","first_page":"215","last_page":"228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.775132417678833},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7118304967880249},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6048063039779663},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5601173043251038},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5085488557815552},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4703429341316223},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4591047763824463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.447307288646698},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3712145686149597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21599331498146057},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1671094000339508}],"concepts":[{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.775132417678833},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7118304967880249},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6048063039779663},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5601173043251038},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5085488557815552},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4703429341316223},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4591047763824463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.447307288646698},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3712145686149597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21599331498146057},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1671094000339508},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tnse.2017.2712064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2017.2712064","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:d-scholarship.pitt.edu:39623","is_oa":false,"landing_page_url":"https://d-scholarship.pitt.edu/39623/9/licenseagreement_dscholarship.txt","pdf_url":null,"source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:1512.03489","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.03489","pdf_url":"https://arxiv.org/pdf/1512.03489","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":null,"raw_type":"text"},{"id":"mag:2195033970","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1512.03489.pdf","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.1512.03489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.03489","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:1512.03489","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.03489","pdf_url":"https://arxiv.org/pdf/1512.03489","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":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W602904462","https://openalex.org/W653925602","https://openalex.org/W1514107797","https://openalex.org/W1536930209","https://openalex.org/W1551177513","https://openalex.org/W1578099820","https://openalex.org/W1586554030","https://openalex.org/W1589331344","https://openalex.org/W1592832583","https://openalex.org/W1783487834","https://openalex.org/W1789701990","https://openalex.org/W1968451201","https://openalex.org/W1972412818","https://openalex.org/W1973836644","https://openalex.org/W1976969221","https://openalex.org/W1978345999","https://openalex.org/W1979356326","https://openalex.org/W1983610133","https://openalex.org/W1994564355","https://openalex.org/W1997698259","https://openalex.org/W2000042664","https://openalex.org/W2001177316","https://openalex.org/W2008620264","https://openalex.org/W2020652754","https://openalex.org/W2033302224","https://openalex.org/W2042479609","https://openalex.org/W2060722488","https://openalex.org/W2067247412","https://openalex.org/W2075984423","https://openalex.org/W2083787309","https://openalex.org/W2088164510","https://openalex.org/W2091322850","https://openalex.org/W2103012681","https://openalex.org/W2104832886","https://openalex.org/W2105850748","https://openalex.org/W2112090702","https://openalex.org/W2112643910","https://openalex.org/W2112976607","https://openalex.org/W2118820208","https://openalex.org/W2119998616","https://openalex.org/W2126927299","https://openalex.org/W2129004493","https://openalex.org/W2129918926","https://openalex.org/W2138855129","https://openalex.org/W2148606196","https://openalex.org/W2152361742","https://openalex.org/W2159929956","https://openalex.org/W2289256326","https://openalex.org/W2318245334","https://openalex.org/W2328187444","https://openalex.org/W2611515161","https://openalex.org/W2611581392","https://openalex.org/W2963678301","https://openalex.org/W2963734869","https://openalex.org/W2963859130","https://openalex.org/W3005919462","https://openalex.org/W3098671236","https://openalex.org/W3103362336","https://openalex.org/W3105441780","https://openalex.org/W3106442811","https://openalex.org/W4230962939","https://openalex.org/W4233413206","https://openalex.org/W4238452917","https://openalex.org/W4243880374","https://openalex.org/W4243997607","https://openalex.org/W4252971074","https://openalex.org/W4312512934","https://openalex.org/W6635318361","https://openalex.org/W6638200967","https://openalex.org/W6644524268","https://openalex.org/W7071288999"],"related_works":["https://openalex.org/W2964227660","https://openalex.org/W3103750149","https://openalex.org/W3104628518","https://openalex.org/W3088059916","https://openalex.org/W2268949487","https://openalex.org/W2008697571","https://openalex.org/W2991293040","https://openalex.org/W2138431798","https://openalex.org/W3105109562","https://openalex.org/W2948108849","https://openalex.org/W2021481737","https://openalex.org/W3106436031","https://openalex.org/W2147453031","https://openalex.org/W2949797716","https://openalex.org/W2790249864","https://openalex.org/W2023399090","https://openalex.org/W2656635310","https://openalex.org/W3103424151","https://openalex.org/W2963758851","https://openalex.org/W2952568974"],"abstract_inverted_index":{"We":[0,42,197],"analyze":[1,233],"the":[2,33,45,48,54,90,117,128,134,146,190,207,210,223,227,234],"eigenvalues":[3,46,132],"of":[4,19,38,47,53,103,127,133,192,226,238],"a":[5,16,39,121,164],"random":[6,40],"graph":[7,55],"ensemble,":[8,56],"proposed":[9],"by":[10,23,110,184],"Chung":[11],"and":[12,79,209],"Lu,":[13],"in":[14,230],"which":[15],"given":[17],"sequence":[18],"<i>expected</i>":[20],"degrees,":[21],"denoted":[22,109],"<inline-formula><tex-math":[24,34,59,65,71,80,92,104,111,123,129,137,168,173,193],"notation=\"LaTeX\">$\\overline{w}_n":[25],"=":[26,74],"(w^{(n)}_1,\\ldots,":[27],"w^{(n)}_n)$</tex-math></inline-formula>":[28],",":[29,69,95,108,115],"is":[30,86,116],"prescribed":[31],"on":[32,44,145,215],"notation=\"LaTeX\">$n$</tex-math>":[35],"</inline-formula>":[36,78,107,171],"nodes":[37,91],"graph.":[41],"focus":[43],"normalized":[49],"(random)":[50],"adjacency":[51],"matrix":[52,136],"defined":[57],"as":[58,172],"notation=\"LaTeX\">$\\mathbf":[60,81,105,112,138,158],"{A}_n$</tex-math></inline-formula>":[61,139],"<inline-formula>":[62,156],"<tex-math":[63,157],"notation=\"LaTeX\">$=$</tex-math></inline-formula>":[64],"notation=\"LaTeX\">$\\sqrt{n\\rho":[66],"_n}[\\mathbf":[67],"{a}^{(n)}_{i,j}]_{i,j=1}^{n}$</tex-math></inline-formula>":[68],"where":[70],"notation=\"LaTeX\">$\\rho":[72],"_n":[73],"1/\\sum":[75],"_{i=1}^{n}":[76],"w^{(n)}_i$</tex-math>":[77],"{a}^{(n)}_{i,j}":[82],"=1$</tex-math></inline-formula>":[83],"if":[84],"there":[85],"an":[87],"edge":[88],"between":[89],"notation=\"LaTeX\">$\\lbrace":[93],"i,j\\rbrace$</tex-math></inline-formula>":[94],"0":[96],"otherwise.":[97],"The":[98],"<i>":[99,165],"empirical":[100,118],"spectral":[101,236],"distribution</i>":[102],"{A}_n$</tex-math>":[106],"{F}_n(\\mathord":[113,159],"{\\cdot})$</tex-math></inline-formula>":[114,160,195],"measure":[119],"putting":[120],"mass":[122],"notation=\"LaTeX\">$1/n$</tex-math></inline-formula>":[124],"at":[125],"each":[126],"notation=\"LaTeX\">$n$</tex-math></inline-formula>":[130],"real":[131],"symmetric":[135],".":[140,176,196],"Under":[141],"some":[142],"technical":[143],"conditions":[144],"expected":[147],"degree":[148,204,212],"sequence,":[149],"we":[150,178,218,232],"show":[151],"that":[152],"with":[153,201],"probability":[154],"one":[155],"converges":[161],"weakly":[162],"to":[163],"deterministic</i>":[166],"distribution":[167,183,237],"notation=\"LaTeX\">$F(\\mathord":[169,194],"{\\cdot})$</tex-math>":[170],"notation=\"LaTeX\">$n\\rightarrow":[174],"\\infty$</tex-math></inline-formula>":[175],"Furthermore,":[177],"fully":[179],"characterize":[180],"this":[181],"deterministic":[182],"providing":[185],"explicit":[186],"closed-form":[187],"expressions":[188],"for":[189],"moments":[191],"illustrate":[198],"our":[199,216],"results":[200],"two":[202],"well-known":[203],"distributions,":[205],"namely,":[206],"power-law":[208,239],"exponential":[211],"distributions.":[213],"Based":[214],"results,":[217],"provide":[219],"significant":[220],"insights":[221],"about":[222],"bulk":[224],"behavior":[225],"eigenvalue":[228],"spectrum;":[229],"particular,":[231],"quasi-triangular":[235],"networks.":[240]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}