Table Of Content(cid:2)
ALGEBRAIC ANALYSIS
OF SOCIAL NETWORKS
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ALGEBRAIC ANALYSIS
OF SOCIAL NETWORKS
Models, Methods & Applications using R
J.AntonioRiveroOstoic
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LibraryofCongressCataloging-in-PublicationData
Names:Ostoic,J.AntonioRivero,author.
Title:Algebraicanalysisofsocialnetworks:models,methods&
applicationsusingR/JAntonioRiveroOstoic.
Description:Hoboken,NJ:Wiley,[2020]|Series:Wileyseriesin
computationalandquantitativesocialscience|Includesindex.
Identifiers:LCCN2020025443(print)|LCCN2020025444(ebook)|ISBN
9781119250388(cloth)|ISBN9781119250326(adobepdf)|ISBN
9781119250395(epub)
Subjects:LCSH:Socialnetworks–Mathematicalmodels.|R(Computerprogram
language)
Classification:LCCHM741.O772020(print)|LCCHM741(ebook)|DDC
302.301/5118–dc23
LCrecordavailableathttps://lccn.loc.gov/2020025443
LCebookrecordavailableathttps://lccn.loc.gov/2020025444
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togitte,santiago,maria-ines
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Contents
ListofFigures xvii
ListofTables xxi
Preface xxiii
Abbreviations xxv
Symbols xxvii
AbouttheCompanionWebsite xxxi
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1 StructuralAnalysiswithAlgebra 1
1.1 Preliminaries 1
1.2 Graphs 2
1.2.1 GraphsandDigraphs 2
1.2.2 Multigraphs 3
1.2.3 SignedGraph 3
1.2.4 BipartiteGraph 4
1.2.5 ValuedGraph 4
1.2.6 MultilevelGraph 5
1.3 Matrices 5
1.3.1 AffiliationMatrix 5
1.3.2 MultipleRelations 6
1.3.3 IncidenceMatrix 6
1.3.4 ValencyMatrix 6
1.3.5 DifferentSystems 7
1.3.6 GraphandMatrixRepresentations 7
1.4 Chains,Paths,andOtherGraphProperties 8
1.5 AlgebraofRelations 9
1.5.1 GeneratorsandCompounds 9
1.6 OperationsonSocialNetworks 10
1.6.1 BinaryOperationonRelations 10
1.6.2 RelationalComposition 11
1.7 TypesandPropertiesofRelations 13
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viii Contents
1.8 EquivalenceandOrdering 14
1.8.1 Equivalence 14
1.8.2 PartialOrder 15
1.8.3 Hierarchy 16
1.9 Functions 16
1.9.1 IdentityandEmptyFunctions 18
1.9.2 Transformations 19
1.10 HomomorphismandCongruence 19
1.10.1 CongruenceRelations 20
1.10.2 KernelofaHomomorphism 20
1.11 StructuralAnalysiswithAlgebra:Summary 21
1.12 LearningStructuralAnalysisbyDoing 22
1.12.1 GettingStarted 22
1.12.2 Matrices 22
1.12.3 Graphs 23
2 AlgebraicStructures 25
2.1 AlgebraicStructureDefinition 25
2.1.1 Closure 25
2.2 GroupStructure 26
2.2.1 CayleyGraph 27
2.2.2 PermutationGroups 28
2.2.3 PresentationofGroupStructures 29
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2.3 GroupofSymmetries:DihedralGroups 30
2.3.1 GroupofSymmetriesoftheEquilateralTriangle 30
2.3.2 GroupofSymmetriesoftheSquare 32
2.3.3 GeneratingSetinSymmetricGroups 34
2.4 Semigroup 34
2.4.1 SemigroupofRelations 35
2.5 SemigroupandGroupProperties 36
2.5.1 RegularElements 36
2.5.2 SubsemigroupsandIdeals 36
2.6 RingandSemiring 37
2.6.1 Semiring 37
2.7 LatticeStructure 38
2.7.1 CongruenceLattice 39
2.7.2 ModularandDistributiveLattice 40
2.8 AlgebraicStructures:Summary 41
2.9 LearningAlgebraicStructuresbyDoing 42
2.9.1 DihedralGroupoftheEquilateralTriangleD 42
3
2.9.2 DihedralGroupoftheSquareD 44
4
2.9.3 ModularandNonmodularLattices 46
3 MultiplexNetworkConfigurations 49
3.1 MultipleNetworks 49
3.1.1 TypesofMultipleNetworks 50
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