Small Worlds

Name: Small Worlds | The Dynamics of Networks between Order and Randomness
Brand: Princeton University Press
Price: 51.49 EUR
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The Dynamics of Networks between Order and Randomness

Duncan J. Watts(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 5. Juni 2018

280 Seiten

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978-0-691-18833-1 (ISBN)

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Inhalt

Cover
Title Page
Copyright Page
Contents
PREFACE
1 Kevin Bacon, the Small World, and Why It All Matters
PART I: STRUCTURE
2 An Overview of the Small-World Phenomenon
2.1 Social Networks and the Small World
2.1.1 A Brief History of the Small World
2.1.2 Difficulties with the Real World
2.1.3 Reframing the Question to Consider All Worlds
2.2 Background on the Theory of Graphs
2.2.1 Basic Definitions
2.2.2 Length and Length Scaling
2.2.3 Neighbourhoods and Distribution Sequences
2.2.4 Clustering
2.2.5 "Lattice Graphs" and Random Graphs
2.2.6 Dimension and Embedding of Graphs
2.2.7 Alternative Definition of Clustering Coefficient
3 Big Worlds and Small Worlds: Models of Graphs
3.1 Relational Graphs
3.1.1 a-Graphs
3.1.2 A Stripped-Down Model: ß-Graphs
3.1.3 Shortcuts and Contractions: Model Invariance
3.1.4 Lies, Damned Lies, and (More) Statistics
3.2 Spatial Graphs
3.2.1 Uniform Spatial Graphs
3.2.2 Gaussian Spatial Graphs
3.3 Main Points in Review
4 Explanations and Ruminations
4.1 Going to Extremes
4.1.1 The Connected-Caveman World
4.1.2 Moore Graphs as Approximate Random Graphs
4.2 Transitions in Relational Graphs
4.2.1 Local and Global Length Scales
4.2.2 Length and Length Scaling
4.2.3 Clustering Coefficient
4.2.4 Contractions
4.2.5 Results and Comparisons with ß-Model
4.3 Transitions in Spatial Graphs
4.3.1 Spatial Length versus Graph Length
4.3.2 Length and Length Scaling
4.3.3 Clustering
4.3.4 Results and Comparisons
4.4 Variations on Spatial and Relational Graphs
4.5 Main Points in Review
5 "It's a Small World after All": Three Real Graphs
5.1 Making Bacon
5.1.1 Examining the Graph
5.1.2 Comparisons
5.2 The Power of Networks
5.2.1 Examining the System
5.2.2 Comparisons
5.3 A Worm's Eye View
5.3.1 Examining the System
5.3.2 Comparisons
5.4 Other Systems
5.5 Main Points in Review
PART II: DYNAMICS
6 The Spread of Infectious Disease in Structured Populations
6.1 A Brief Review of Disease Spreading
6.2 Analysis and Results
6.2.1 Introduction of the Problem
6.2.2 Permanent-Removal Dynamics
6.2.3 Temporary-Removal Dynamics
6.3 Main Points in Review
7 Global Computation in Cellular Automata
7.1 Background
7.1.1 Global Computation
7.2 Cellular Automata on Graphs
7.2.1 Density Classification
7.2.2 Synchronisation
7.3 Main Points in Review
8 Cooperation in a Small World: Games on Graphs
8.1 Background
8.1.1 The Prisoner's Dilemma
8.1.2 Spatial Prisoner's Dilemma
8.1.3 N-Player Prisoner's Dilemma
8.1.4 Evolution of Strategies
8.2 Emergence of Cooperation in a Homogeneous Population
8.2.1 Generalised Tit-for-Tat
8.2.2 Win-Stay, Lose-Shift
8.3 Evolution of Cooperation in a Heterogeneous Population
8.4 Main Points in Review
9 Global Synchrony in Populations of Coupled Phase Oscillators
9.1 Background
9.2 Kuramoto Oscillators on Graphs
9.3 Main Points in Review
10 Conclusions
Notes
Bibliography
Index

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