{"id":"https://openalex.org/W2767729178","doi":"https://doi.org/10.1093/comnet/cnx055","title":"Entrograms and coarse graining of dynamics on complex networks","display_name":"Entrograms and coarse graining of dynamics on complex networks","publication_year":2017,"publication_date":"2017-10-17","ids":{"openalex":"https://openalex.org/W2767729178","doi":"https://doi.org/10.1093/comnet/cnx055","mag":"2767729178"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnx055","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnx055","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.01987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Mauro Faccin","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Mauro Faccin","raw_affiliation_strings":["Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre, 4, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre, 4, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Michael T Schaub","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Michael T Schaub","raw_affiliation_strings":["Institute for Data, Systems, and Society Massachusetts Institute of Technology, 77 Massachusetts Avenue Cambridge, MA, USA and Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Data, Systems, and Society Massachusetts Institute of Technology, 77 Massachusetts Avenue Cambridge, MA, USA and Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jean-Charles Delvenne","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Jean-Charles Delvenne","raw_affiliation_strings":["Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM) and Center for Operations Research and Econometrics (CORE), Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre, 4, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM) and Center for Operations Research and Econometrics (CORE), Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre, 4, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.3001,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.55464136,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"6","issue":"5","first_page":"661","last_page":"678"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.37220001220703125,"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":0.37220001220703125,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.10040000081062317,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.03189999982714653,"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/granularity","display_name":"Granularity","score":0.7770000100135803},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5949000120162964},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.5295000076293945},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4830999970436096},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4787999987602234},{"id":"https://openalex.org/keywords/network-dynamics","display_name":"Network dynamics","score":0.47049999237060547},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.46209999918937683},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45500001311302185},{"id":"https://openalex.org/keywords/evolving-networks","display_name":"Evolving networks","score":0.3598000109195709},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.35359999537467957}],"concepts":[{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.7770000100135803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6622999906539917},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5949000120162964},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5608000159263611},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.5295000076293945},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4830999970436096},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4787999987602234},{"id":"https://openalex.org/C123757187","wikidata":"https://www.wikidata.org/wiki/Q9195957","display_name":"Network dynamics","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.46209999918937683},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4553999900817871},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C36647736","wikidata":"https://www.wikidata.org/wiki/Q5418752","display_name":"Evolving networks","level":3,"score":0.3598000109195709},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.32190001010894775},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.3043999969959259},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28360000252723694},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2671000063419342},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25999999046325684},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.2556000053882599},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.25200000405311584},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1093/comnet/cnx055","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnx055","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.01987","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.01987","pdf_url":"https://arxiv.org/pdf/1711.01987","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":"pmh:oai:dial.uclouvain.be:boreal:194699","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/194699","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Complex Networks, (2017)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.01987","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.01987","pdf_url":"https://arxiv.org/pdf/1711.01987","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":[],"awards":[{"id":"https://openalex.org/G5979967617","display_name":"Higher-order interactions and Laplacian dynamics in complex networks: structure, dynamics and control","funder_award_id":"702410","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767729178.pdf","grobid_xml":"https://content.openalex.org/works/W2767729178.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1532729789","https://openalex.org/W1954262271","https://openalex.org/W1962338095","https://openalex.org/W1964846359","https://openalex.org/W1967184357","https://openalex.org/W1978825280","https://openalex.org/W1979857612","https://openalex.org/W1989450361","https://openalex.org/W1994360749","https://openalex.org/W1995996823","https://openalex.org/W2001996043","https://openalex.org/W2012662151","https://openalex.org/W2021046139","https://openalex.org/W2021812458","https://openalex.org/W2036613247","https://openalex.org/W2038195874","https://openalex.org/W2044988896","https://openalex.org/W2045021315","https://openalex.org/W2050766178","https://openalex.org/W2051638434","https://openalex.org/W2066636486","https://openalex.org/W2067573658","https://openalex.org/W2070722739","https://openalex.org/W2075694080","https://openalex.org/W2090463147","https://openalex.org/W2092040152","https://openalex.org/W2095293504","https://openalex.org/W2104319764","https://openalex.org/W2119998616","https://openalex.org/W2132515640","https://openalex.org/W2132914434","https://openalex.org/W2139818818","https://openalex.org/W2152284345","https://openalex.org/W2157547297","https://openalex.org/W2164998314","https://openalex.org/W2168346701","https://openalex.org/W2232939579","https://openalex.org/W2265944008","https://openalex.org/W2510701725","https://openalex.org/W2513567506","https://openalex.org/W2566971417","https://openalex.org/W2606554761","https://openalex.org/W2951271819","https://openalex.org/W3101413764","https://openalex.org/W3124443731","https://openalex.org/W4231009334","https://openalex.org/W4232095703","https://openalex.org/W6633811599","https://openalex.org/W6658883175","https://openalex.org/W6677111876","https://openalex.org/W6735855921","https://openalex.org/W6789375458"],"related_works":[],"abstract_inverted_index":{"Using":[0],"an":[1,245],"information":[2,155,161,246],"theoretic":[3,162,247],"point":[4],"of":[5,23,36,73,112,121,137,210,218,240,273,282],"view,":[6],"we":[7,27,124,253],"investigate":[8,199],"how":[9,31,154,181,200],"a":[10,14,37,42,55,58,79,90,103,127,138,171,189,225,242,263,266,283],"dynamics":[11,56,106,184,213,234],"acting":[12,286],"on":[13,45,57,228,255,287],"network":[15,243],"can":[16,185,278],"be":[17,63,87,186,259],"coarse":[18,65,80,98,139,219,275],"grained":[19,66,140,220,276],"through":[20],"the":[21,33,46,74,94,109,113,119,144,165,174,178,183,196,206,211,229,238,288],"use":[22,195],"graph":[24,60,209],"partitions.":[25],"Specifically,":[26],"are":[28],"interested":[29],"in":[30,93,177,205,215,235],"aggregating":[32],"state":[34],"space":[35],"Markov":[38,110,192,284],"process":[39,239,285],"according":[40],"to":[41,102,130,198],"partition":[43,85],"impacts":[44],"thus":[47],"obtained":[48],"lower-dimensional":[49,105],"dynamics.":[50],"We":[51,194,222],"highlight":[52,270],"that":[53,68,107,126,257,271],"for":[54,173],"particular":[59],"there":[61],"may":[62,86,100,258],"multiple":[64],"descriptions":[67,277],"capture":[69,279],"different,":[70],"incomparable":[71],"features":[72],"original":[75,114,212],"process.":[76,115,193],"For":[77],"instance,":[78],"graining":[81,99],"induced":[82],"by":[83,188,261],"one":[84],"commensurate":[88],"with":[89],"time-scale":[91],"separation":[92],"dynamics,":[95],"while":[96],"another":[97],"correspond":[101],"different":[104,280],"preserves":[108],"property":[111],"Taking":[116],"inspiration":[117],"from":[118,244],"literature":[120],"Computational":[122],"Mechanics,":[123],"find":[125],"convenient":[128],"tool":[129],"summarize":[131],"and":[132,233,237,269],"visualize":[133],"such":[134],"dynamical":[135],"properties":[136,217],"model":[141],"(partition)":[142],"is":[143],"entrogram.":[145],"The":[146],"entrogram":[147,197],"gathers":[148],"certain":[149],"information-theoretic":[150],"measures,":[151],"which":[152],"quantify":[153],"flows":[156],"across":[157],"time":[158],"steps.":[159],"These":[160],"quantities":[163],"include":[164],"entropy":[166],"rate,":[167],"as":[168,170],"well":[169,182],"measure":[172],"memory":[175],"contained":[176],"process,":[179],"i.e.,":[180],"approximated":[187,260],"first":[190],"order":[191],"specific":[201],"macro-scale":[202],"connection":[203],"patterns":[204],"state\u2013space":[207],"transition":[208],"result":[214],"desirable":[216],"descriptions.":[221],"thereby":[223],"provide":[224],"fresh":[226],"perspective":[227],"interplay":[230],"between":[231],"structure":[232],"networks,":[236],"partitioning":[241],"perspective.":[248],"To":[249],"illustrate":[250],"our":[251],"points,":[252],"focus":[254],"networks":[256],"both":[262],"core-periphery":[264],"or":[265],"clustered":[267],"organization,":[268],"each":[272],"these":[274],"aspects":[281],"network.":[289]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2017-11-17T00:00:00"}
