Models, Methods and Applications Using R
Buch, Englisch, 416 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 892 g
ISBN: 978-1-119-25038-8
Verlag: Wiley
Presented in a comprehensive manner, this book provides a comprehensive foundation in algebraic approaches for the analysis of different types of social networks such as multiple, signed, and affiliation networks. The study of such configurations corresponds to the structural analysis within the social sciences, and the methods applied for the analysis are in the areas of abstract algebra, combinatorics, and graph theory.
Current research in social networks has moved toward the examination of more realistic but also more complex social relations by which agents or actors are connected in multiple ways. Addressing this trend, this book offers hands-on training of the algebraic procedures presented along with the computer package multiplex, written by the book’s author specifically to perform analyses of multiple social networks. An introductory section on both complex networks and for R will feature, however the subjects themselves correspond to advanced courses on social network analysis with the specialization on algebraic models and methods.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
List of Figures xvii
List of Tables xxi
Preface xxiii
Abbreviations xxv
Symbols xxvii
About the Companion Website xxxi
1 Structural Analysis with Algebra 1
1.1 Preliminaries 1
1.2 Graphs 2
1.2.1 Graphs and Digraphs 2
1.2.2 Multigraphs 3
1.2.3 Signed Graph 3
1.2.4 Bipartite Graph 4
1.2.5 Valued Graph 4
1.2.6 Multilevel Graph 5
1.3 Matrices 5
1.3.1 Affiliation Matrix 5
1.3.2 Multiple Relations 6
1.3.3 Incidence Matrix 6
1.3.4 Valency Matrix 6
1.3.5 Different Systems 7
1.3.6 Graph and Matrix Representations 7
1.4 Chains, Paths, and Other Graph Properties 8
1.5 Algebra of Relations 9
1.5.1 Generators and Compounds 9
1.6 Operations on Social Networks 10
1.6.1 Binary Operation on Relations 10
1.6.2 Relational Composition 11
1.7 Types and Properties of Relations 13
1.8 Equivalence and Ordering 14
1.8.1 Equivalence 14
1.8.2 Partial Order 15
1.8.3 Hierarchy 16
1.9 Functions 16
1.9.1 Identity and Empty Functions 18
1.9.2 Transformations 19
1.10 Homomorphism and Congruence 19
1.10.1 Congruence Relations 20
1.10.2 Kernel of a Homomorphism 20
1.11 Structural Analysis with Algebra: Summary 21
1.12 Learning Structural Analysis by Doing 22
1.12.1 Getting Started 22
1.12.2 Matrices 22
1.12.3 Graphs 23
2 Algebraic Structures 25
2.1 Algebraic Structure Definition 25
2.1.1 Closure 25
2.2 Group Structure 26
2.2.1 Cayley Graph 27
2.2.2 Permutation Groups 28
2.2.3 Presentation of Group Structures 29
2.3 Group of Symmetries: Dihedral Groups 30
2.3.1 Group of Symmetries of the Equilateral Triangle 30
2.3.2 Group of Symmetries of the Square 32
2.3.3 Generating Set in Symmetric Groups 34
2.4 Semigroup 34
2.4.1 Semigroup of Relations 35
2.5 Semigroup and Group Properties 36
2.5.1 Regular Elements 36
2.5.2 Subsemigroups and Ideals 36
2.6 Ring and Semiring 37
2.6.1 Semiring 37
2.7 Lattice Structure 38
2.7.1 Congruence Lattice 39
2.7.2 Modular and Distributive Lattice 40
2.8 Algebraic Structures: Summary 41
2.9 Learning Algebraic Structures by Doing 42
2.9.1 Dihedral Group of the Equilateral Triangle D3 42
2.9.2 Dihedral Group of the Square D4 44
2.9.3 Modular and Nonmodular Lattices 46
3 Multiplex Network Configurations 49
3.1 Multiple Networks 49
3.1.1 Types of Multiple Networks 50
3.2 Kinship Networks and Group Structure 51
3.2.1 Marriage Types in Kinship Systems 52
3.3 Rules for Marriage and Descent in the Kariera Society 53
3.3.1 Group Structure and Set of Equations 55
3.4 Algebraic Constraints 56
3.5 Link Generalizations and Complex Structures 57
3.6 Bundle Patterns 58
3.6.1 Bundle Class Properties 59
3.6.2 Bundle Isomorphic Classes 60
3.6.3 Statistical Approach to Bundle Patterns 61
3.7 Co-occurrence of Ties Model 62
3.8 Relational Structure 64
3.8.1 Strength of Weak Ties Model as Relational Structure 65
3.8.2 Graph Representation of the Strength of Weak Ties 66
3.9 Semigroup of Relations in Multiplex Networks 68
3.9.1 Partial Order Relations and the Axiom of Quality 69
3.9.2 Multiplication Table 71
3.10 Partially Ordered Semigroup 74
3.10.1 Partial Ordering in XZ 75
3.11 Word and Edge Tables 76
3.12 Multiplex Network Configurations: Summary 77
3.13 Learning Multiplex Networks by Doing 78
3.13.1 Kariera Kinship Network 78
3.13.2 Multiplex Networks 79
3.13.3 Strength of Weak Ties 80
3.13.4 Relational Structure 80
4 Positional Analysis and Role Structure 83
4.1 Roles and Positions 83
4.2 Network Homomorphism 84
4.2.1 Weak and Strong Graph Homomorphisms 85
4.2.2 Juncture Graph Homomorphism 86
4.3 Global Equivalences 87
4.3.1 Structural Equivalence 88
4.3.2 Automorphic Equivalence 88
4.3.3 Regular Equivalence 89
4.3.4 Generalized Equivalence 90
4.4 Global Equivalences Applied 91
4.5 Local Equivalences 94
4.5.1 Relation-Box R(W) 94
4.5.2 Relation Plane and Role Relations in R(W) 95
4.5.3 Local Role Equivalence 96
4.6 Compositional Equivalence 97
4.6.1 Formal Definition of Compositional Equivalence 98
4.7 Positional Analysis with Compositional Equivalence 99
4.7.1 Cumulated Person Hierarchy, H 99
4.7.2 Set of Generators in Complex Networks 101
4.7.3 Incorporating Actor Attributes 102
4.8 Positional Analysis and Role Structure: Summary 104
4.9 Learning Positional Analysis and Role Structure by Doing 105
4.9.1 Equivalence Relations 105
5 Role Structure in Multiplex Networks 109
5.1 Directed Role Structures: Incubator Network A 110
5.1.1 Social Positions in Network XA 111
5.1.2 Modeling XA with Compositional Equivalence 112
5.1.3 Cumulated Person Hierarchy HA 114
5.1.4 Positional System SA 116
5.2 Role Structure Incubator Network A 119
5.2.1 Constructing Role Structures 120
5.2.2 Particular Elements in the Role Structure 121
5.2.3 Role Structure with Relational Contrast 122
5.3 Undirected Role Structures: Florentine Families Network 125
5.3.1 Positional Analysis of the Florentine Families Network 125
5.3.2 Constructing Person Hierarchies, HF 127
5.3.3 Family Attributes in XF 129
5.4 Role Structure of the Florentine Families Network 132
5.4.1 Interlock of Business, Marriage and Wealth Role Relations in QF 134
5.4.2 Inclusion of Role Relations 135
5.5 Role Structure in Multiplex Networks: Summary 137
5.6 Learning Role Stru
