Fundamentals of complex networks : models, structures, and dynamics

385 Pages·2015·19.702 MB·English

by  Chen, Guanrong, Li, Xiang, Wang, Xiaofan

FUNDAMENTALS OF
COMPLEX NETWORKS

FUNDAMENTALS OF
COMPLEX NETWORKS
MODELS, STRUCTURES
AND DYNAMICS
GuanrongChen
CityUniversityofHongKong,China
Xiaofan Wang
ShanghaiJiaoTongUniversity,Shanghai,China
XiangLi
FudanUniversity,Shanghai,China
Thiseditionfirstpublished2015
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LibraryofCongressCataloging-in-PublicationData
Chen,G.(Guanrong)
Fundamentalsofcomplexnetworks:models,structures,anddynamics/GuanrongChen,Xiaofan
Wang,XiangLi.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-71811-7(cloth)
1.Systemtheory.I.Wang,Xiaofan,1967–II.Li,Xiang,1976February8–III.Title.
Q295.C45242015
003′.72–dc23
2014034304
Typesetin10/12ptTimesLTStdbyLaserwordsPrivateLimited,Chennai,India
1 2015
Contents
AbouttheAuthors xi
Preface xiii
Acknowledgements xv
PartI FUNDAMENTALTHEORY
1 Introduction 3
1.1 BackgroundandMotivation 3
1.2 ABriefHistoryofComplexNetworkResearch 5
1.2.1 TheKönigsburgSeven-BridgeProblem 5
1.2.2 RandomGraphTheory 7
1.2.3 Small-WorldExperiments 7
1.2.4 StrengthsofWeakTies 10
1.2.5 HeterogeneityandtheWWW 10
1.3 NewEraofComplex-NetworkStudies 11
Exercises 13
References 13
2 Preliminaries 15
2.1 ElementaryGraphTheory 15
2.1.1 Background 15
2.1.2 BasicConcepts 15
2.1.3 Adjacency,IncidenceandLaplacianMatrices 24
2.1.4 DegreeCorrelationandAssortativity 26
2.1.5 SomeBasicResultsonGraphs 31
2.1.6 EulerianandHamiltonianGraphs 35
2.1.7 PlaneandPlanarGraphs 37
2.1.8 TreesandBipartiteGraphs 39
2.1.9 DirectedGraphs 41
2.1.10 WeightedGraphs 45
2.1.11 SomeApplications 46
2.2 ElementaryProbabilityandStatistics 52
2.2.1 ProbabilityPreliminaries 52
2.2.2 StatisticsPreliminaries 58
2.2.3 LawofLargeNumbersandCentralLimitTheorem 59
2.2.4 MarkovChains 61
vi Contents
2.3 ElementaryDynamicalSystemsTheory 62
2.3.1 BackgroundandMotivation 62
2.3.2 SomeAnalyticalTools 70
2.3.3 ChaosinNonlinearSystems 72
2.3.4 Kolmogorov-SinaiEntropy 77
2.3.5 SomeExamplesofChaoticSystems 78
2.3.6 StabilitiesofNonlinearSystems 85
Exercises 90
References 100
3 NetworkTopologies:BasicModelsandProperties 103
3.1 Introduction 103
3.2 RegularNetworks 103
3.3 ERRandom-GraphModel 105
3.4 Small-WorldNetworkModels 108
3.4.1 WSSmall-WorldNetworkModel 108
3.4.2 NWSmall-WorldNetworkModel 108
3.4.3 StatisticalPropertiesofSmall-WorldNetworkModels 109
3.5 NavigableSmall-WorldNetworkModel 112
3.6 Scale-FreeNetworkModels 114
3.6.1 BAScale-FreeNetworkModel 114
3.6.2 RobustnessversusFragility 118
3.6.3 ModifiedBAModels 122
3.6.4 ASimpleModelwithPower-LawDegreeDistribution 126
3.6.5 Local-WorldandMulti-Local-WorldNetworkModels 126
Exercises 133
References 135
PartII APPLICATIONS-SELECTEDTOPICS
4 Internet:TopologyandModeling 139
4.1 Introduction 139
4.2 TopologicalPropertiesoftheInternet 141
4.2.1 Power–LawNode-DegreeDistribution 141
4.2.2 HierarchicalStructure 143
4.2.3 Rich-ClubStructure 145
4.2.4 DisassortativeProperty 147
4.2.5 CorenessandBetweenness 148
4.2.6 GrowthoftheInternet 151
4.2.7 Router-LevelInternetTopology 152
4.2.8 GeographicLayoutoftheInternet 153
4.3 Random-GraphNetworkTopologyGenerator 155
4.4 StructuralNetworkTopologyGenerators 156
4.4.1 TiersTopologyGenerator 157
4.4.2 Transit–StubTopologyGenerator 158
4.5 Connectivity-BasedNetworkTopologyGenerators 159
4.5.1 Inet 160
4.5.2 BRITEModel 161
4.5.3 GLPModel 163
4.5.4 PFPModel 165
4.5.5 T Model 166
ANG
Contents vii
4.6 Multi-Local-WorldModel 167
4.6.1 TheoreticalConsiderations 167
4.6.2 NumericalResultswithComparison 169
4.6.3 PerformanceComparison 176
4.7 HOTModel 178
4.8 DynamicalBehaviorsoftheInternetTopologicalCharacteristics 181
4.9 TrafficFluctuationonWeightedNetworks 181
4.9.1 WeightedNetworks 183
4.9.2 GRDModel 183
4.9.3 DataTrafficFluctuations 184
References 190
5 EpidemicSpreadingDynamics 195
5.1 Introduction 195
5.2 EpidemicThresholdTheory 196
5.2.1 Epidemic(SI,SIS,SIR)Models 196
5.2.2 EpidemicThresholdsonHomogenousNetworks 197
5.2.3 StatisticalDataAnalysis 198
5.2.4 EpidemicThresholdsonHeterogeneousNetworks 199
5.2.5 EpidemicThresholdsonBANetworks 200
5.2.6 EpidemicThresholdsonFinite-SizedScale-FreeNetworks 202
5.2.7 EpidemicThresholdsonCorrelatedNetworks 202
5.2.8 SIRModelofEpidemicSpreading 203
5.2.9 EpidemicSpreadingonQuenchedNetworks 205
5.3 EpidemicSpreadingonSpatialNetworks 206
5.3.1 SpatialNetworks 206
5.3.2 SpatialNetworkModelsforInfectiousDiseases 207
5.3.3 ImpactofSpatialClusteringonDiseaseTransmissions 209
5.3.4 Large-ScaleSpatialEpidemicSpreading 211
5.3.5 ImpactofHumanLocation-SpecificContactPatterns 212
5.4 ImmunizationonComplexNetworks 213
5.4.1 RandomImmunization 213
5.4.2 TargetedImmunization 213
5.4.3 AcquaintanceImmunization 215
5.5 ComputerVirusSpreadingovertheInternet 215
5.5.1 RandomConstant-SpreadModel 216
5.5.2 ACompartment-BasedModel 217
5.5.3 SpreadingModelsofEmailViruses 219
5.5.4 EffectsofComputerVirusonNetworkTopologies 221
References 222
6 CommunityStructures 225
6.1 Introduction 225
6.1.1 VariousScenariosinReal-WorldSocialNetworks 225
6.1.2 GeneralizationofAssortativity 226
6.2 CommunityStructureandModularity 230
6.2.1 CommunityStructure 230
6.2.2 Modularity 230
6.2.3 ModularityofWeightedandDirectedNetworks 233
6.3 Modularity-BasedCommunityDetectingAlgorithms 234
6.3.1 CNMScheme 234
6.3.2 BGLLScheme 236
viii Contents
6.3.3 Multi-SliceCommunityDetection 237
6.3.4 DetectingSpatialCommunityStructures 240
6.4 OtherCommunityPartitioningSchemes 240
6.4.1 LimitationsoftheModularityMeasure 240
6.4.2 CliquePercolationScheme 242
6.4.3 Edge-BasedCommunityDetectionScheme 244
6.4.4 EvaluationCriteriaforCommunityDetectionAlgorithms 249
6.5 SomeRecentProgress 253
References 253
7 NetworkGames 257
7.1 Introduction 257
7.2 Two-Player/Two-StrategyEvolutionaryGamesonNetworks 261
7.2.1 IntroductiontoGamesonNetworks 261
7.2.2 Two-Player/Two-StrategyGamesonRegularLattices 261
7.2.3 Two-Player/Two-StrategyGamesonBAScale-FreeNetworks 264
7.2.4 Two-Player/Two-StrategyGamesonCorrelatedScale-FreeNetworks 267
7.2.5 Two-Player/Two-StrategyGamesonClusteredScale-FreeNetworks 271
7.3 Multi-Player/Two-StrategyEvolutionaryGamesonNetworks 273
7.3.1 IntroductiontoPublicGoodsGame 273
7.3.2 Multi-Player/Two-StrategyEvolutionaryGamesonBANetworks 273
7.3.3 Multi-Player/Two-StrategyEvolutionaryGamesonCorrelatedScale-free
Networks 276
7.3.4 Multi-Player/Two-StrategyEvolutionaryGamesonClusteredScale-free
Networks 280
7.4 AdaptiveEvolutionaryGamesonNetworks 284
References 286
8 NetworkSynchronization 289
8.1 Introduction 289
8.2 CompleteSynchronizationofContinuous-TimeNetworks 290
8.2.1 CompleteSynchronizationofGeneralContinuous-TimeNetworks 293
8.2.2 CompleteSynchronizationofLinearlyCoupledContinuous-TimeNetworks 297
8.3 CompleteSynchronizationofSomeTypicalDynamicalNetworks 299
8.3.1 CompleteSynchronizationofRegularNetworks 300
8.3.2 SynchronizationofSmall-WorldNetworks 301
8.3.3 SynchronizationofScale-FreeNetworks 302
8.3.4 CompleteSynchronizationofLocal-WorldNetworks 306
8.4 PhaseSynchronization 306
8.4.1 PhaseSynchronizationoftheKuramotoModel 308
8.4.2 PhaseSynchronizationofSmall-WorldNetworks 310
8.4.3 PhaseSynchronizationofScale-FreeNetworks 310
8.4.4 PhaseSynchronizationofNonuniformlyCoupledNetworks 314
References 316
9 NetworkControl 319
9.1 Introduction 319
9.2 SpatiotemporalChaosControlonRegularCML 319
9.3 PinningControlofComplexNetworks 322
9.3.1 AugmentedNetworkApproach 322
9.3.2 PinningControlofScale-FreeNetworks 323