{"id":"https://openalex.org/W2099570416","doi":"https://doi.org/10.1080/15427951.2008.10129304","title":"The Structure of Geographical Threshold Graphs","display_name":"The Structure of Geographical Threshold Graphs","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2099570416","doi":"https://doi.org/10.1080/15427951.2008.10129304","mag":"2099570416"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2008.10129304","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129304","pdf_url":"https://www.internetmathematicsjournal.com/article/1455.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1455.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061939453","display_name":"Milan Bradonji\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Milan Bradonji\u0107","raw_affiliation_strings":["Department of Electrical Engineering, UCLA, Los Angeles, CA 90095 and Mathematical Modeling and Analysis Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, UCLA, Los Angeles, CA 90095 and Mathematical Modeling and Analysis Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002373487","display_name":"Aric Hagberg","orcid":"https://orcid.org/0000-0003-2327-3725"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aric Hagberg","raw_affiliation_strings":["Theoretical Division, Mathematical Modeling and Analysis Group, Los Alamos National Laboratory, Los Alamos, NM 87545"],"affiliations":[{"raw_affiliation_string":"Theoretical Division, Mathematical Modeling and Analysis Group, Los Alamos National Laboratory, Los Alamos, NM 87545","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040226358","display_name":"Allon G. Percus","orcid":"https://orcid.org/0000-0002-0847-5284"},"institutions":[{"id":"https://openalex.org/I136722135","display_name":"Claremont Graduate University","ror":"https://ror.org/0157pnt69","country_code":"US","type":"education","lineage":["https://openalex.org/I136722135"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Allon G. Percus","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095 and School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095 and School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711","institution_ids":["https://openalex.org/I136722135"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061939453"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":1.9672,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.86531764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1-2","first_page":"113","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":1.0,"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":1.0,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9944999814033508,"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":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9051600098609924},{"id":"https://openalex.org/keywords/clustering-coefficient","display_name":"Clustering coefficient","score":0.6934786438941956},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6266812086105347},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.615199625492096},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6074641942977905},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.6012108325958252},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5858776569366455},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5726224184036255},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48635274171829224},{"id":"https://openalex.org/keywords/giant-component","display_name":"Giant component","score":0.4843076765537262},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.47063443064689636},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.46683469414711},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.44924020767211914},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44795548915863037},{"id":"https://openalex.org/keywords/percolation","display_name":"Percolation (cognitive psychology)","score":0.43243786692619324},{"id":"https://openalex.org/keywords/percolation-threshold","display_name":"Percolation threshold","score":0.4223087430000305},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.42041486501693726},{"id":"https://openalex.org/keywords/preferential-attachment","display_name":"Preferential attachment","score":0.4110734760761261},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.27347320318222046},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20608118176460266},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.17381784319877625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16485583782196045},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13471943140029907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9051600098609924},{"id":"https://openalex.org/C22047676","wikidata":"https://www.wikidata.org/wiki/Q898680","display_name":"Clustering coefficient","level":3,"score":0.6934786438941956},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6266812086105347},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.615199625492096},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6074641942977905},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.6012108325958252},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5858776569366455},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5726224184036255},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48635274171829224},{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.4843076765537262},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.47063443064689636},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.46683469414711},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.44924020767211914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44795548915863037},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.43243786692619324},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.4223087430000305},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.42041486501693726},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.4110734760761261},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.27347320318222046},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20608118176460266},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.17381784319877625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16485583782196045},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13471943140029907},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.0},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/15427951.2008.10129304","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129304","pdf_url":"https://www.internetmathematicsjournal.com/article/1455.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1259158600","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1259158600","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"pmh:oai:CiteSeerX.psu:10.1.1.156.5747","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.5747","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ee.ucla.edu/~milan/pubs/intmath09.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2008.10129304","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129304","pdf_url":"https://www.internetmathematicsjournal.com/article/1455.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1630165961","display_name":"EMT/MISC: Collaborative Research: Harnessing Statistical Physics for Computing and Communication","funder_award_id":"0829945","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1872210597","display_name":null,"funder_award_id":"DE-AC52-06NA2539","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2031045238","display_name":null,"funder_award_id":"DE-AC52-06NA253","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G359075050","display_name":null,"funder_award_id":"DE-AC52-06NA25396","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3700687868","display_name":null,"funder_award_id":"AC52-06NA25396","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G5083158263","display_name":null,"funder_award_id":"DE-AC52-06NA25396","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5657628048","display_name":null,"funder_award_id":"AC52-06NA25396","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6932788750","display_name":null,"funder_award_id":"DE-AC52-06NA25396","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G75892134","display_name":null,"funder_award_id":"DE-AC52-06NA25396","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8527529014","display_name":null,"funder_award_id":"DE-AC52-06NA2539","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G928841278","display_name":null,"funder_award_id":"contract DE-AC52-06NA25396","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2099570416.pdf","grobid_xml":"https://content.openalex.org/works/W2099570416.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W108214179","https://openalex.org/W630423399","https://openalex.org/W1526841711","https://openalex.org/W1568371145","https://openalex.org/W1570340896","https://openalex.org/W1660264423","https://openalex.org/W1976969221","https://openalex.org/W1979170109","https://openalex.org/W1981101107","https://openalex.org/W1993255855","https://openalex.org/W2008620264","https://openalex.org/W2044881936","https://openalex.org/W2051132263","https://openalex.org/W2056380633","https://openalex.org/W2068871408","https://openalex.org/W2097147952","https://openalex.org/W2113233457","https://openalex.org/W2113701578","https://openalex.org/W2115579680","https://openalex.org/W2129620481","https://openalex.org/W2139975838","https://openalex.org/W2150596521","https://openalex.org/W2905110430","https://openalex.org/W2997134027","https://openalex.org/W3143219376","https://openalex.org/W4285719527","https://openalex.org/W4301476203"],"related_works":["https://openalex.org/W4297311514","https://openalex.org/W2949141875","https://openalex.org/W2950867090","https://openalex.org/W2896261814","https://openalex.org/W2535608133","https://openalex.org/W2127010026","https://openalex.org/W3102102810","https://openalex.org/W1580095423","https://openalex.org/W2041715914","https://openalex.org/W2315206337"],"abstract_inverted_index":{"We":[0,48,70],"analyze":[1],"the":[2,9,37,51,64,74,78,90,98,118],"structure":[3],"of":[4,18,82,89],"random":[5,19],"graphs":[6],"generated":[7],"by":[8],"geographical":[10],"threshold":[11,34,65,75],"model.":[12],"The":[13],"model":[14],"is":[15,112],"a":[16,33,83,104],"generalization":[17],"geometric":[20],"graphs.":[21],"Nodes":[22],"are":[23,29,121],"distributed":[24],"in":[25],"space,":[26],"and":[27,55,60,67,87,92],"edges":[28],"assigned":[30],"according":[31],"to":[32,63,115],"function":[35],"involving":[36],"distance":[38],"between":[39],"nodes":[40,102],"as":[41,43],"well":[42],"randomly":[44],"chosen":[45],"node":[46,119],"weights.":[47],"show":[49],"how":[50],"degree":[52,106],"distribution,":[53],"percolation":[54],"connectivity":[56,86],"transitions,":[57],"clustering":[58,99],"coefficient,":[59],"diameter":[61],"relate":[62],"value":[66,76],"weight":[68],"distribution.":[69],"give":[71],"bounds":[72],"on":[73],"guaranteeing":[77],"presence":[79],"or":[80],"absence":[81],"giant":[84],"component,":[85],"disconnectivity":[88],"graph,":[91],"small":[93],"diameter.":[94],"Finally,":[95],"we":[96],"consider":[97],"coefficient":[100],"for":[101],"with":[103],"given":[105],"_l_,":[107],"finding":[108],"that":[109],"its":[110],"scaling":[111],"very":[113],"close":[114],"1/_l_":[116],"when":[117],"weights":[120],"exponentially":[122],"distributed.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
