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Tables of Contents for Small Worlds
Chapter/Section Title
Page #
Page Count
Preface
xiii
Kevin Bacon, the Small World, and Why It All Matters
3
6
Part I Structure
9
154
An Overview of the Small-World Phenomenon
11
30
Social Networks and the Small World
11
14
A Brief History of the Small World
12
8
Difficulties with the Real World
20
4
Reframing the Question to Consider All Worlds
24
1
Background on the Theory of Graphs
25
16
Basic Definitions
25
2
Length and Length Scaling
27
4
Neighbourhoods and Distribution Sequences
31
1
Clustering
32
1
``Lattice Graphs'' and Random Graphs
33
6
Dimension and Embedding of Graphs
39
1
Alternative Definition of Clustering Coefficient
40
1
Big Worlds and Small Worlds: Models of Graphs
41
60
Relational Graphs
42
49
α-Graphs
42
24
A Stripped-Down Model: β-Graphs
66
4
Shortcuts and Contractions: Model Invariance
70
17
Lies, Damned Lies, and (More) Statistics
87
4
Spatial Graphs
91
9
Uniform Spatial Graphs
93
5
Gaussian Spatial Graphs
98
2
Main Points in Review
100
1
Explanations and Ruminations
101
37
Going to Extremes
101
13
The Connected-Caveman World
102
7
Moore Graphs as Approximate Random Graphs
109
5
Transitions in Relational Graphs
114
13
Local and Global Length Scales
114
2
Length and Length Scaling
116
1
Clustering Coefficient
117
1
Contractions
118
2
Results and Comparisons with β-Model
120
7
Transitions in Spatial Graphs
127
6
Spatial Length versus Graph Length
127
1
Length and Length Scaling
128
2
Clustering
130
2
Results and Comparisons
132
1
Variations on Spatial and Relational Graphs
133
3
Main Points in Review
136
2
``It's a Small World after All'': Three Real Graphs
138
25
Making Bacon
140
7
Examining the Graph
141
2
Comparisons
143
4
The Power of Networks
147
6
Examining the System
147
3
Comparisons
150
3
A Worm's Eye View
153
6
Examining the System
154
2
Comparisons
156
3
Other Systems
159
2
Main Points in Review
161
2
Part II Dynamics
163
80
The Spread of Infectious Disease in Structured Populations
165
16
A Brief Review of Disease Spreading
166
2
Analysis and Results
168
12
Introduction of the Problem
168
1
Permanent-Removal Dynamics
169
7
Temporary-Removal Dynamics
176
4
Main Points in Review
180
1
Global Computation in Cellular Automata
181
18
Background
181
6
Global Computation
184
3
Cellular Automata on Graphs
187
11
Density Classification
187
8
Synchronisation
195
3
Main Points in Review
198
1
Cooperation in a Small World: Games on Graphs
199
24
Background
199
9
The Prisoner's Dilemma
200
4
Spatial Prisoner's Dilemma
204
2
N-Player Prisoner's Dilemma
206
1
Evolution of Strategies
207
1
Emergence of Cooperation in a Homogeneous Population
208
11
Generalised Tit-for-Tat
209
5
Win-Stay, Lose-Shift
214
5
Evolution of Cooperation in a Heterogeneous Population
219
2
Main Points in Review
221
2
Global Synchrony in Populations of Coupled Phase Oscillators
223
17
Background
223
5
Kuramoto Oscillators on Graphs
228
10
Main Points in Review
238
2
Conclusions
240
3
Notes
243
6
Bibliography
249
8
Index
257