Community Structure of Complex Networks

126 Pages·2013·2.274 MB·English

by  Hua-Wei Shen (auth.)

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Hua-Wei Shen
Community
Structure of
Complex Networks
Author Supervisor
Dr.Hua-WeiShen Prof.Xue-QiCheng
InstituteofComputingTechnology InstituteofComputingTechnology
ChineseAcademyofSciences ChineseAcademyofScience
Beijing,China Beijing,China
ISSN2190-5053 ISSN2190-5061(electronic)
SpringerTheses
ISBN978-3-642-31820-7 ISBN978-3-642-31821-4(eBook)
DOI10.1007/978-3-642-31821-4
SpringerHeidelbergNewYorkDordrechtLondon
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To my dearest wife Yü-Yü Cheng, and our
lovelysonJun-HaoShen.
Supervisor’s Foreword
We are now surrounded by the ubiquitous complex networks, varying from the
World Wide Web to the booming online social networks, from the power grid to
thetransportationnetwork,fromthecommunicationnetworkstovariouseconomic
networks,fromthenetworkswithincellororganismtothenetworkofecosystem.
Thesenetworksarefromvariousdisciplines,constructedfordifferentpurposes,and
seemtobeunrelatedtoeachother.However,thesenetworksexhibitastoundinggen-
eralcharacteristics,includingthesmall-worldphenomenonandthepower-lawde-
greedistribution.Itistherighttimetosaythat“thenetworktakeover”.Meanwhile,
comprehensive research on complex networks requires the revolution of method-
ology. The reductionism,as a paradigm, is expired. The graph theory, as a mathe-
matical discipline, hits the limit. From the perspective of complexity and with the
networkthinking,data-drivenmethodologyisdevelopingintoanewdiscipline,i.e.,
networkscience.
Asasalientstructuralcharacteristicofcomplexnetworks,communitystructure
indicatestheregularityoftopologicalstructureandreflectsthelocalityofrelation-
shipsamongthecomponentsofnetworks.Communitystructureisfundamentalto
manyfunctionalfeaturesofcomplexnetworks,suchastherobustnessandnaviga-
bility.Moreover,communitystructureaffectsorevendeterminesthebehaviorofthe
dynamicalprocessestakingplaceonnetworks,includingtheinformationdiffusion,
thespreadofdiseaseandrumor,andsynchronization.Therefore,communitystruc-
ture is crucial to understanding the relation between the structure and function of
complexnetworksandhasimportanttheoreticalandpracticalimplicationstoutilize
andcontrolthedynamicson,orof,thecomplexnetworks.
This book focuses on the community structure of complex networks. In partic-
ular,thisbookprovidesaclearreviewfortheresearchadvancesinthecommunity
detection of networks, which is one of the hottest research topics in network sci-
ence. In this book, the author studies four critical aspects of communitystructure.
Thefouraspectsaretheoverlapsamongcommunities,themultiscaleofcommunity
structure,therelationshipbetweencommunitystructureandnetworkdynamics,and
thecoexistenceofmultipletypesofstructuralregularitiesbeyondcommunitystruc-
ture. Aiming to investigate the community structure in real world networks, this
vii
viii Supervisor’sForeword
book first highlights the limitation of modularity optimization, which is a classic
methodforcommunitydetection.Theauthorfirstproposesthealgorithmtosimul-
taneously detect the overlapping and hierarchical community structure. Then, the
author proposes a dimensionality reduction framework for uncovering the multi-
scale community structure in networks with heterogeneous networks. Further, the
authorstudiesthediffusiondynamicsonnetworksandrevealstherelationshipbe-
tweenthetabletransientsindiffusionprocessandtheintrinsiccommunitystructure
innetworks.Finally,theauthorexploresthemultipletypesofstructuralregularities
innetworksusingprobabilisticgraphicalmodel.Mostofthepreliminaryworksof
thisbookhavebeenpublishedinprestigiousjournalsonnetworkscience,e.g.,the
Physical Review E, and Journal of Statistical Mechanics. This book is also heav-
ily based on Dr. Shen’s doctoral thesis, but with a substantial expansion based on
hisfollow-upresearch.Dr.Shen’sthesiswascompletedinResearchCenterforRe-
searchCenterforWebDataScienceandEngineering,InstituteofComputingTech-
nology,ChineseAcademyofSciences.Thisthesiswashonoredwiththe“Top100
Excellent Doctoral Dissertations Award” from the Chinese Academy of Sciences
andwasnominatedasthe“OutstandingDoctoralDissertation”bytheChineseCom-
puterFederation.Ingeneral,thisbookbringstogethertherecentresearcheffortsof
Dr.Sheninthefieldofcommunitystructureinnetworks.
I believe both the researchers and practitioners in the field of social network
analysisandthebroaderareaofnetworksciencecanbenefitfromreadingthisbook.
Moreover, this book shows the research track of Dr. Shen from a Ph.D. student to
aprofessor,whichmaybeofinterestparticularlytonewPh.D.students.Iwantto
complimentDr.Shenforhavingwrittensuchanoutstandingbookforthenetwork
sciencecommunity.
InstituteofComputingTechnology,Beijing,China Xue-QiCheng
Acknowledgements
This book was partially supported by the National Natural Science Foundation
of China (NSFC) under grant Nos. 61232010, 61202215, 60873245, 60872036,
60933005,60873217,and60803123,andtheNationalBasicResearchProgramof
China (the 973 program) under grant Nos. 2004CB318109, 2007CB310805, and
2012CB316303,andtheNationalHigh-TechR&DProgramofChina(the863pro-
gram)undergrantNos.2006AA01Z452and2010AA012502,andtheBeijingNat-
uralScienceFoundationundergrantNo.4122077.Thisbookwasalsosupportedby
KeyLabofInformationNetworkSecurity,MinistryofPublicSecurity.
Theauthorwouldalsoliketothankthesupportsfromvariousresearchcenters,
including: (1) Research Center of Web Data Science and Engineering, Institute of
ComputingTechnology,ChineseAcademyofSciences;(2)KeyLabofInformation
NetworkSecurity,MinistryofPublicSecurity.
ix
Parts of This Book Have Been Published
in the Following Articles
Shen, H.W., Cheng, X.Q., Cai, K., Hu, M.B.: Detect overlapping and hierarchical
community structure in networks. Physica A 388(8), 1706–1712 (2009) (Repro-
ducedwithPermission)
Shen, H.W., Cheng, X.Q., Guo, J.F.: Quantifying and identifying the overlapping
communitystructureinnetworks.J.Stat.Mech.P07042(2009)(Reproducedwith
Permission)
Shen,H.W.,Cheng,X.Q.,Fang,B.X.:Covariance,correlationmatrix,andthemul-
tiscale communitystructure of networks. Phys. Rev. E 82, 016114 (2010) (Repro-
ducedwithPermission)
Shen,H.W.,Cheng,X.Q.:Spectralmethodsforthedetectionofnetworkcommunity
structure: a comparative analysis. J. Stat. Mech. P10020 (2010) (Reproduced with
Permission)
Shen,H.W.,Cheng,X.Q.:Uncoveringthecommunitystructureassociatedwiththe
diffusion dynamics on networks. J. Stat. Mech. P04024 (2010) (Reproduced with
Permission)
Shen, H.W., Cheng, X.Q., Guo, J.F.: Exploring the structural regularities in net-
works.Phys.Rev.E84,056111(2011)(ReproducedwithPermission)
Shen,H.W.,Cheng,X.Q.,Wang,Y.Z.,Chen,Y.:Adimensionalityreductionframe-
work for detection of multiscale structure in heterogeneous networks. J. Comput.
Sci.Technol.27,341–357(2012)(ReproducedwithPermission)
xi
Contents
1 CommunityStructure:AnIntroduction . . . . . . . . . . . . . . . . 1
1.1 NetworkScience:AnEmergingDiscipline . . . . . . . . . . . . . 1
1.2 Community Structure: An Salient Structural Characteristic
ofNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 ABriefReviewforCommunityDetection . . . . . . . . . . . . . 3
1.3.1 WhatIsaCommunity? . . . . . . . . . . . . . . . . . . . 4
1.3.2 CommunityDetection . . . . . . . . . . . . . . . . . . . . 6
1.3.3 CommunityValidity . . . . . . . . . . . . . . . . . . . . . 11
1.4 ConcludingRemarks. . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 DetectingtheOverlappingandHierarchicalCommunityStructure
inNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 EAGLE:DetectingtheOverlappingandHierarchicalCommunity
Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 TheAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 ExtendingModularitytoQuantifytheOverlappingCommunity
Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 QuantifyingtheOverlappingCommunityStructure . . . . 30
2.3.2 IdentifyingtheOverlappingCommunityStructure . . . . . 32
2.3.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 ConclusionsandDiscussions . . . . . . . . . . . . . . . . . . . . 42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 MultiscaleCommunityDetectioninNetworkswithHeterogeneous
DegreeDistributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 PrincipalComponentAnalysis . . . . . . . . . . . . . . . 46
xiii