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

Cover -- Title Page -- Copyright -- Contents -- List of Figures -- List of Tables -- Preface -- Abbreviations -- Symbols -- About the Companion Website -- Chapter 1 Structural Analysis with Algebra -- 1.1 Preliminaries -- 1.2 Graphs -- 1.2.1 Graphs and Digraphs -- 1.2.2 Multigraphs -- 1.2.3 Signed Graph -- 1.2.4 Bipartite Graph -- 1.2.5 Valued Graph -- 1.2.6 Multilevel Graph -- 1.3 Matrices -- 1.3.1 Affiliation Matrix -- 1.3.2 Multiple Relations -- 1.3.3 Incidence Matrix -- 1.3.4 Valency Matrix -- 1.3.5 Different Systems -- 1.3.6 Graph and Matrix Representations -- 1.4 Chains, Paths, and Other Graph Properties -- 1.5 Algebra of Relations -- 1.5.1 Generators and Compounds -- 1.6 Operations on Social Networks -- 1.6.1 Binary Operation on Relations -- 1.6.2 Relational Composition -- 1.7 Types and Properties of Relations -- 1.8 Equivalence and Ordering -- 1.8.1 Equivalence -- 1.8.2 Partial Order -- 1.8.3 Hierarchy -- 1.9 Functions -- 1.9.1 Identity and Empty Functions -- 1.9.2 Transformations -- 1.10 Homomorphism and Congruence -- 1.10.1 Congruence Relations -- 1.10.2 Kernel of a Homomorphism -- 1.11 Structural Analysis with Algebra: Summary -- 1.12 Learning Structural Analysis by Doing -- 1.12.1 Getting Started -- 1.12.2 Matrices -- 1.12.3 Graphs -- Chapter 2 Algebraic Structures -- 2.1 Algebraic Structure Definition -- 2.1.1 Closure -- 2.2 Group Structure -- 2.2.1 Cayley Graph -- 2.2.2 Permutation Groups -- 2.2.3 Presentation of Group Structures -- 2.3 Group of Symmetries: Dihedral Groups -- 2.3.1 Group of Symmetries of the Equilateral Triangle -- 2.3.2 Group of Symmetries of the Square -- 2.3.3 Generating Set in Symmetric Groups -- 2.4 Semigroup -- 2.4.1 Semigroup of Relations -- 2.5 Semigroup and Group Properties -- 2.5.1 Regular Elements -- 2.5.2 Subsemigroups and Ideals -- 2.6 Ring and Semiring -- 2.6.1 Semiring -- 2.7 Lattice Structure.