{"id":"https://openalex.org/W2151919492","doi":"https://doi.org/10.1109/tit.2011.2155618","title":"Graph-Theoretical Constructions for Graph Entropy and Network Coding Based Communications","display_name":"Graph-Theoretical Constructions for Graph Entropy and Network Coding Based Communications","publication_year":2011,"publication_date":"2011-07-11","ids":{"openalex":"https://openalex.org/W2151919492","doi":"https://doi.org/10.1109/tit.2011.2155618","mag":"2151919492"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2155618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2155618","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://durham-repository.worktribe.com/output/1522556","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037486046","display_name":"Maximilien Gadouleau","orcid":"https://orcid.org/0000-0003-4701-738X"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Maximilien Gadouleau","raw_affiliation_strings":["School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, UK"],"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, UK","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005137861","display_name":"S\u00f8ren Riis","orcid":"https://orcid.org/0000-0003-0697-4116"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S\u00f8ren Riis","raw_affiliation_strings":["School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, UK"],"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, UK","institution_ids":["https://openalex.org/I166337079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037486046"],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":null,"apc_paid":null,"fwci":5.2511,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.95832162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"10","first_page":"6703","last_page":"6717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9523000121116638,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.927299976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.8925824165344238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6299266815185547},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5962046980857849},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.5786560773849487},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5501329898834229},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5099488496780396},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4534100294113159},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.44870439171791077},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.4428861439228058},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3302456736564636},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.32038694620132446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3129245936870575},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.3053790330886841}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8925824165344238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6299266815185547},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5962046980857849},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.5786560773849487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5501329898834229},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5099488496780396},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4534100294113159},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.44870439171791077},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.4428861439228058},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3302456736564636},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.32038694620132446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3129245936870575},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.3053790330886841},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2011.2155618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2155618","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:durham-repository.worktribe.com:1522556","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1522556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/22923","is_oa":false,"landing_page_url":"http://qmro.qmul.ac.uk/xmlui/handle/123456789/22923","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:durham-repository.worktribe.com:1522556","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1522556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2660577913","display_name":null,"funder_award_id":"EP/H016015/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W67153351","https://openalex.org/W86626612","https://openalex.org/W606453859","https://openalex.org/W1562379951","https://openalex.org/W1563286165","https://openalex.org/W1606480398","https://openalex.org/W1650455072","https://openalex.org/W1988856559","https://openalex.org/W2004159513","https://openalex.org/W2041588219","https://openalex.org/W2048235391","https://openalex.org/W2098674643","https://openalex.org/W2103320637","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2113940092","https://openalex.org/W2119442443","https://openalex.org/W2130512442","https://openalex.org/W2133338663","https://openalex.org/W2134955799","https://openalex.org/W2137806147","https://openalex.org/W2138928022","https://openalex.org/W2140678653","https://openalex.org/W2142293082","https://openalex.org/W2150284816","https://openalex.org/W2161792498","https://openalex.org/W2163322487","https://openalex.org/W2167703619","https://openalex.org/W2171844485","https://openalex.org/W3142269533","https://openalex.org/W4238591275"],"related_works":["https://openalex.org/W2954009223","https://openalex.org/W1568744482","https://openalex.org/W4379539820","https://openalex.org/W2366079443","https://openalex.org/W1927597435","https://openalex.org/W2793949464","https://openalex.org/W2014355235","https://openalex.org/W153309283","https://openalex.org/W2380035736","https://openalex.org/W2741713059"],"abstract_inverted_index":{"The":[0],"guessing":[1,36,55,69,85,121,143,154,183,211],"number":[2,70,82,144,184,212,215,238],"of":[3,12,24,48,61,71,79,83,123,145,164,173,189,199,216,239],"a":[4,18,25,72,94,107,124,161,171,235],"directed":[5],"graph":[6,43,122],"(digraph),":[7],"equivalent":[8],"to":[9,52,76,129,138,186,219],"the":[10,22,35,49,54,59,68,77,80,97,110,116,120,142,187,190,206,209,214,244,257],"entropy":[11],"that":[13,67,112],"digraph,":[14,50,126],"was":[15],"introduced":[16],"as":[17,53],"direct":[19],"criterion":[20],"on":[21,34,44,96,109,141,179],"solvability":[23,90],"network":[26,88,157,231],"coding":[27,89,158,232],"instance.":[28],"This":[29],"paper":[30],"makes":[31],"two":[32],"contributions":[33],"number.":[37],"First,":[38],"we":[39,134,148],"introduce":[40],"an":[41,196],"undirected":[42],"all":[45],"possible":[46],"configurations":[47],"referred":[51],"graph,":[56],"which":[57,205,243],"encapsulates":[58],"essence":[60],"dependence":[62],"amongst":[63],"configurations.":[64],"We":[65,168,193],"prove":[66],"digraph":[73],"is":[74,91,104],"equal":[75,185],"logarithm":[78],"independence":[81],"its":[84],"graph.":[86],"Therefore,":[87],"no":[92],"more":[93],"problem":[95,108],"operations":[98,246],"made":[99],"by":[100],"each":[101],"node,":[102],"but":[103],"simplified":[105],"into":[106],"messages":[111],"can":[113,166],"transit":[114],"through":[115],"network.":[117],"By":[118],"studying":[119],"given":[125],"and":[127,213,249,256],"how":[128],"combine":[130],"digraphs":[131,151,174,200,223],"or":[132],"alphabets,":[133],"are":[135,247,254,259],"thus":[136],"able":[137],"derive":[139],"bounds":[140],"digraphs.":[146],"Second,":[147],"construct":[149,195],"specific":[150],"with":[152,175,182,201,234],"high":[153],"numbers,":[155],"yielding":[156],"instances":[159,233,253],"where":[160],"large":[162],"amount":[163],"information":[165],"transit.":[167],"first":[169],"propose":[170],"construction":[172],"finite":[176],"parameters":[177],"based":[178],"cyclic":[180],"codes,":[181],"degree":[188],"generator":[191],"polynomial.":[192],"then":[194],"infinite":[197],"class":[198],"arbitrary":[202],"girth":[203],"for":[204,242],"ratio":[207],"between":[208],"linear":[210],"vertices":[217],"tends":[218],"one,":[220],"despite":[221],"these":[222,252],"being":[224],"arbitrarily":[225,260],"sparse.":[226],"These":[227],"constructions":[228],"yield":[229],"solvable":[230],"relatively":[236],"small":[237],"intermediate":[240],"nodes":[241],"node":[245],"known":[248],"linear,":[250],"although":[251],"sparse":[255],"sources":[258],"far":[261],"from":[262],"their":[263],"corresponding":[264],"sinks.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}