Table of contents;
List of Figures ix
List of Tables xiii
Preface xv
Chapter 1.
Introduction
1 Epidemics
2 Residential Segregation
6 Exercises 11
Chapter 2. Set Theory and Mathematical Truth
12 Boolean Algebra and Overlapping Groups
19 Truth and Falsity in Mathematics
21 Exercises
23 Chapter 3.
Probability: Pure and Applied
25 Example: Gambling
28 Two or More Events: Conditional Probabilities
29 Two or More Events: Independence
30 A Counting Rule: Permutations and Combinations
31 The Binomial Distribution
32 Exercises
36 Chapter 4.
Relations and Functions
38 Symmetry
41 Reflexivity
43 Transitivity
44 Weak Orders-Power and Hierarchy
45 Equivalence Relations
46 Structural Equivalence
47 Transitive Closure:
The Spread of Rumors and Diseases
49 Exercises
51 Chapter 5.
Networks and Graphs
53 Exercises
59 Chapter 6.
Weak Ties 61 Bridges
61 The Strength of Weak Ties
62 Exercises
66 Chapter 7.
Vectors and Matrices
67 Sociometric Matrice
69 Probability Matrices
71 The Matrix, Transposed
72 Exercises
72 Chapter 8
Adding and Multiplying Matrices
74 Multiplication of Matrices
75 Multiplication of Adjacency Matrices
77 Locating Cliques
79 Exercises
82 Chapter 9
Cliques and Other Groups
84 Blocks
86 Exercises
87 Chapter 10.
Centrality
89 Degree Centrality
93 Graph Center 93 Closeness Centrality
94 Eigenvector Centrality
95 Betweenness Centrality
96 Centralization
99 Exercises
101 Chapter 11.
Small-World Networks
102 Short Network Distances
103 Social Clustering
105 The Small-World Network Model
111 Exercises
116 Chapter 12.
Scale-Free Networks
117 Power-Law Distribution
118 Preferential Attachment
121 Network Damage and Scale-Free Networks
129 Disease Spread in Scale-Free Networks
134 Exercises
136 Chapter 13.
Balance Theory
137 Classic Balance Theory
137 Structural Balance
145 Exercises
148 The Markov Assumption: History Does Not Matter
156 Transition Matrices and Equilibrium
157 Exercises
158 Chapter 15.
Demography
161 Mortality 162 Life Expectancy
167 Fertility
171 Population Projection
173 Exercises 179 Chapter 16
Evolutionary Game Theory
180 Iterated Prisoner's Dilemma
184 Evolutionary Stability
185 Exercises
188 Chapter 17
. Power and Cooperative Games
190 The Kernel
195 The Core
199 Exercises
200 Chapter 18.
Complexity and Chaos
202 Chaos 202 Complexity
206 Exercises
212 Afterword: "Resistance Is Futile"
213 Bibliography
217 Index 219