Algebraic analysis of social networks : models, methods & applications using R

목차 (Table of Contents)

• CONTENTS
• 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
• 1.3 Matrices = 5
• 1.4 Chains, Paths, and Other Graph Properties = 8
• 1.5 Algebra of Relations = 9
• 1.6 Operations on Social Networks = 10
• 1.7 Types and Properties of Relations = 13
• 1.8 Equivalence and Ordering = 14
• 1.9 Functions = 16
• 1.10 Homomorphism and Congruence = 19
• 1.11 Structural Analysis with Algebra : Summary = 21
• 1.12 Learning Structural Analysis by Doing = 22
• 2 Algebraic Structures = 25
• 2.1 Algebraic Structure Definition = 25
• 2.2 Group Structure = 26
• 2.3 Group of Symmetries : Dihedral Groups = 30
• 2.4 Semigroup = 34
• 2.5 Semigroup and Group Properties = 36
• 2.6 Ring and Semiring = 37
• 2.7 Lattice Structure = 38
• 2.8 Algebraic Structures: Summary = 41
• 2.9 Learning Algebraic Structures by Doing = 42
• 3 Multiplex Network Configurations = 49
• 3.1 Multiple Networks = 49
• 3.2 Kinship Networks and Group Structure = 51
• 3.3 Rules for Marriage and Descent in the Kariera Society = 53
• 3.4 Algebraic Constraints = 56
• 3.5 Link Generalizations and Complex Structures = 57
• 3.6 Bundle Patterns = 58
• 3.7 Co-occurrence of Ties Model = 62
• 3.8 Relational Structure = 64
• 3.9 Semigroup of Relations in Multiplex Networks = 68
• 3.10 Partially Ordered Semigroup = 74
• 3.11 Word and Edge Tables = 76
• 3.12 Multiplex Network Configurations : Summary = 77
• 3.13 Learning Multiplex Networks by Doing = 78
• 4 Positional Analysis and Role Structure = 83
• 4.1 Roles and Positions = 83
• 4.2 Network Homomorphism = 84
• 4.3 Global Equivalences = 87
• 4.4 Global Equivalences Applied = 91
• 4.5 Local Equivalences = 94
• 4.6 Compositional Equivalence = 97
• 4.7 Positional Analysis with Compositional Equivalence = 99
• 4.8 Positional Analysis and Role Structure : Summary = 104
• 4.9 Learning Positional Analysis and Role Structure by Doing = 105
• 5 Role Structure in Multiplex Networks = 109
• 5.1 Directed Role Structures : Incubator Network A = 110
• 5.2 Role Structure Incubator Network A = 119
• 5.3 Undirected Role Structures : Florentine Families Network = 125
• 5.4 Role Structure of the Florentine Families Network = 132
• 5.5 Role Structure in Multiplex Networks : Summary = 137
• 5.6 Learning Role Structure in Multiplex Networks by Doing = 138
• 6 Decomposition of Role Structures = 145
• 6.1 Aggregation and Decomposition = 145
• 6.2 Synthesis Rules = 147
• 6.3 Lattice of Congruence Relations = 149
• 6.4 Factorization = 150
• 6.5 Congruences by Substitution Property = 152
• 6.6 Aggregation of Role Structures in QA = 153
• 6.7 Role Interlock of Incubator Network A = 159
• 6.8 Progressive Homomorphic Reduction of Factors in QA = 166
• 6.9 Role Structure for Incubator Network B = 169
• 6.10 Role Interlock of Incubator Network C = 172
• 6.11 Role Interlock of =QF for Florentine Families Network = 173
• 6.12 Reduction Diagram = 177
• 6.13 Decomposition of Role Structures : Summary = 179
• 6.14 Learning Decomposition of Role Structures by Doing = 180
• 7 Signed Networks = 187
• 7.1 Structural Analysis of Signed Networks = 187
• 7.2 Social Influence Process = 188
• 7.3 Structural Balance = 191
• 7.4 Semirings for Structural Balance = 195
• 7.5 Balance and Comparison Influence = 199
• 7.6 Looking for Structural Balance = 201
• 7.7 Signed Networks: Summary = 209
• 7.8 Learning Signed Networks by Doing = 210
• 8 Affiliation Networks = 215
• 8.1 Structural Analysis of Affiliation Networks = 215
• 7.2 Binomial Projection = 218
• 8.2 Common Affiliations = 220
• 8.3 Formal Concept Analysis = 224
• 8.4 Formal Concepts and Galois Derivations = 225
• 8.5 Concept Lattice and Ordering of Concepts = 228
• 8.6 Order Filters and Order Ideals = 232
• 8.7 Affiliation Networks : Summary = 234
• 8.8 Learning Affiliation Networks by Doing = 235
• 9 Valued Networks = 241
• 9.1 Relational Structure of Valued Networks = 242
• 9.2 Many-valued Contexts = 249
• 9.3 Pathfinder Network Analysis = 255
• 9.4 Pathfinder Semiring to Co-affiliation Network in XB20 = 258
• 9.5 Triangle Inequality = 259
• 9.6 Trade Network XVG20 with Triangle Inequality = 262
• 9.7 Valued Networks : Summary = 264
• 9.8 Learning Valued Networks by Doing = 265
• 10 Multilevel Networks = 273
• 10.1 Structural Analysis of Multilevel Systems = 273
• 10.2 Visual Representation of Clients and Attorneys Multilevel Network = 274
• 10.3 Multilevel Structure of the G20 Network = 276
• 10.4 Multilevel Positional System of G20 Network with Bridges = 279
• 10.5 Algebraic Approaches to Multilevel Networks = 284
• 10.6 Reducing Complexity in XMG20b = 289
• 10.7 Further Algebraic Representations of Multilevel Structures = 291
• 10.8 Multilevel Networks : Summary = 292
• 10.9 Learning Multilevel Networks by Doing = 293
• 11 Comparing Relational Structures = 301
• 11.1 Comparing Structures with Algebraic Constraints = 302
• 11.2 Incubator Networks B and C = 303
• 11.3 Equality = 307
• 11.4 Hierarchy of Relations = 310
• 11.5 Shared Structure by Role Tables = 312
• 11.6 Semigroup Tables with Joint Homomorphic Reduction = 316
• 11.7 Comparison Across Networks with Common Structure Semigroup = 319
• 11.8 Comparing Structures in Substantial Terms = 324
• 11.9 Structuring Effect of Role Relations in Incubators = 327
• 11.10 Comparing Relational Structures : Summary = 329
• 11.11 Learning Comparing Relational Structures by Doing = 330
• A Datasets = 335
• Kariera kinship = 335
• Incubators A, B, C = 335
• Florentine families = 336
• Clients and attorneys = 336
• Group of twenty = 336
• B Role structures of Incubator networks = 339
• Role Structure of XA = 339
• Role Structure of XB = 339
• Positional system of Incubator network B = 339
• Role tables in QB = 341
• Role Structure of XC = 342
• Positional system of Incubator network C = 342
• C Valued data in G20 Trade network = 347
• Group of Twenty Indicators = 347
• Commodities in G20 Trade valued network = 348
• Units of measure ofG20 country data = 348
• G20 Trade valued network and salient structures = 348
• D Layout visualization algorithms = 353
• Force-directed = 353
• Stress-majorization = 355
• Laplacian Function = 358
• New stress internal function = 359
• E Role structure workflow = 361
• Decomposition of Role structure 2B = 361
• Incubator network B = 361
• Positional analysis and Role structure = 361
• Factorization = 362
• Progressive factorization of Factors = 363
• Aggregated structure of 2B = 370
• Bibliography = 371
• Index = 377