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The structure of complex networks: theory and applications PDF

478 Pages·2016·9.514 MB·English
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THE STRUCTURE OF COMPLEX NETWORKS This page intentionally left blank The Structure of Complex Networks TheoryandApplications ERNESTO ESTRADA 1 3 GreatClarendonStreet,Oxfordox26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork (cid:2)c OxfordUniversityPress2011 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) Firstpublished2011 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable TypesetbySPIPublisherServices,Pondicherry,India PrintedinGreatBritain onacid-freepaperby CPIGroup(UK)Ltd,Croydon,CR04YY ISBN 978–0–19–959175–6 10 9 8 7 6 5 4 3 2 1 ToGissell,Doris,andPuri This page intentionally left blank Preface “Ifyouwanttounderstandfunction,studystructure”. F.H.C.Crick The idea of writing this book arose in Venice in the summer of 2009, while I was attending the scientific conference NetSci09. This international work- shoponnetworksciencewasmainlyattendedbyphysicistswhowerestudying thestructureanddynamicsofcomplexnetworks.Ihadpreviouslyattendeda workshop in Rio de Janeiro devoted to spectral graph theory and its applica- tions,whichwasmainlyattendedbymathematicians.Althoughthetwoareas are very much overlapped, the language, approaches, and results presented there were almost disjointed. It is frequently read that the study of complex networksisatrulyinterdisciplinaryresearchfield.However,itishardtofinda bookthatreallyreflectsthischaracter,unifyingthelanguagesandresultsused ingraphtheoryandnetworkscience.Thesituationisevenmorecomplicated ifweconsiderthatmanypractitionersofnetworkscienceworkinapplication areassuchaschemistry,ecology,molecularandcellularbiology,engineering, andsocio-economicsciences.Theresultofthismeltingpotisthatmanyresults are duplicated in different areas, usually with different denominations, and morecriticallythereisalackofunificationofthefieldtoformanindependent scientificdisciplinethatcanbeproperlycalled‘networkscience’. Thisbookisamodestcontributiontothedevelopmentofaunifiednetwork theory.Ihavetriedtoexpressinacommonlanguagetheresultsfromalgebraic, topological,metrical,andextremalgraphtheory,withtheconceptsdeveloped instatisticalmechanicsandmolecularphysics,andenrichedwithmanyideas and formulations developed in mathematical chemistry, biology, and social sciences. All these concepts are first mathematically formulated, and then explained and illustrated with simple examples from artificial and real-world networks. This comprises the first part of this volume, which is specifically devoted to the development of network theory. The second part is dedicated to applications in different fields, including the study of biochemical and molecular biology networks, anatomical networks, ecological networks, and socioeconomic networks. The idea of these chapters is not to describe a few resultspreviously reportedintheliteraturebutrathertocriticallyanalyse the roleofnetworktheoryintacklingrealproblemsinthesefields.Thenexamples of successful applications of network theory in these fields are illustrated, while erroneous applications and interpretations are critically analysed—the overallideabeingtopresentaunifiedpictureofthefieldofnetworkscience. That is, I consider these application areas as being at the intersection of the scientificdisciplinesandnetworktheorywheretheproblemsarise. Whystudythestructureofnetworks?ThequotefromFrancisH.C.Crick, co-discovererofthestructureofDNA,andNobellaureate,isself-explanatory. viii Preface This is the real ethos of this book. Of course, it is hard to define what we understandby‘structure’,andasmallsectionisdevotedtoadiscussionofthis intheintroductorychapter.However,evenwithoutacompleteunderstanding ofthisconcept,architects,scientists,andartistshaveshapedourworldaswe see it today. Children usually open their toys to ‘see their internal structures’ inanattempttounderstandhowtheywork.Knowingthestructureofcomplex networksdoesnotguaranteethatweautomaticallyunderstandhowtheywork, but without this knowledge it is certainly impossible to advance our under- standingoftheirfunctioning.Thisbookisdevotedtothecharacterisationofthe structureofnetworksbasedonacombinationofmathematicalapproachesand physical analogies. This characterisation is still incomplete, and more effort is needed in the unification of apparently disconnected concepts. The reader is encouraged to take this route to advance to a definitive theory of complex networks.Finally,Ihavetriedtocorrecterrorsandmisconceptionsfoundhere andthereacrossallfieldsinwhichnetworksarestudied,frommathematicsto biology.However,Iwouldbepleasedtobenotifiedofanythingwhichmight requirecorrection. This book was written mainly in Glasgow (UK), but some parts were written in Remedios (Cuba) and Santiago de Compostela (Spain). Through- out this time I had the support of many colleagues and friends, as well as my family, although mentioning all of them would be an impossible task. However, I would like to express my gratitude to all my past and present collaborators—those who have shared datasets, software, and figures which are used in this book, or who have contributed in some way with one or other part of the process of writing: A. Allendes, U. Alon, N. A. Alves, C. Atilgan, S. R. Aylward, G. Bagler, A.-L. Baraba´si, V. Batagelj, M. Benzi, A.G.Bunn,D.Bassett,P.A.Bates,M.Bogun˜a´,C.CagatayBilgin,P.Cheb- otarev,J.Crofts,J.A.Dunne,L.daFontouraCosta,J.delosRios,K.-I.Goh, L. H. Greene, R. Guimera`, N. Hatano, Y. He, D. J. Higham, E. Koonin, D.- S.Lee,M.Martin,R.Milo,J.Moody,M.E.J.Newman,P.Pereira,A.Perna, E. Ravasz, J. A. Rodr´ıguez-Velazquez, R. Singh, R. V. Sole´, O. Sporn, S. J. Stuart, M. Takayasu, H. Takayasu, V. van Noort, E. Vargas, and D. J. Watts. I also want to thank all the members of my family—in particular, Puri—for their infinite patience. Last but not least, I thank S. Adlung, A. Warman, and C.CharlesatOxfordUniversityPressfortheireffectivesupport. ErnestoEstrada Glasgow,3February,2011 Contents PartI Theory 1 1 Introduction 3 1.1 Whatarenetworks? 3 1.2 Whendidthestorybegin? 4 1.3 Aformaldefinition 6 1.4 Whydowestudytheirstructure? 9 1.5 Howcanwespeaktheir‘language’? 14 2 Adjacencyrelationsinnetworks 25 2.1 Nodeadjacencyrelationship 25 2.2 Degreedistributions 27 2.3 Degree–degreecorrelations 31 2.4 Linkadjacencyandbeyond 36 2.5 DiscreteLaplacianoperator 37 2.6 Spectralpropertiesofnetworks 39 3 Metricandtopologicalstructureofnetworks 47 3.1 Shortestpathdistance 47 3.2 Resistancedistance 50 3.3 Generalizednetworkdistances 55 3.4 Topologicalstructureofnetworks 57 4 Fragments(subgraphs)incomplexnetworks 73 4.1 Network‘graphlets’ 74 4.2 Networkmotifs 76 4.3 Closedwalksandsubgraphs 78 4.4 Countingsmallundirectedsubgraphsanalytically 79 4.5 Fragmentratios 82 5 Accountingforallparts(subgraphs) 89 5.1 TheEstradaindex 90 5.2 ParameterisedEstradaindex 95 5.3 Networkentropyandfreeenergy 97 5.4 Networkreturnability 103 5.5 Abriefonmatrixfunctions 106

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