Analyzing Narratives in Social Networks: Taking Turing to the Arts

Description

This book uses literature as a wrench to pry open social networks and to ask different questions than have been asked about social networks previously. The book emphasizes the story-telling aspect of social networks, as well as the connection between narrative and social networks by incorporating narrative, dynamic networks, and time. Thus, it constructs a bridge between literature, digital humanities, and social networks. This book is a pioneering work that attempts to express social and philosophic constructs in mathematical terms. The material used to test the algorithms is texts intended for performance, such as plays, film scripts, and radio plays; mathematical representations of the texts, or “literature networks”, are then used to analyze the social networks found in the respective texts. By using literature networks and their accompanying narratives, along with their supporting analyses, this book allows for a novel approach to social network analysis. Preface Introduction How to Read This Book Download Materials Overview Synopsis Acknowledgements Words of Thanks Contents 1 Overview of the Book 1.1 Introduction 1.2 Brief Notes on Notation and Definitions 1.3 The Role of Interpretation in Literature and Math 1.4 Social Clocks 1.5 Psychology-Driven Algorithms 1.6 Looking Ahead Part I Static Literature Networks 2 Graphs in Dramas 2.1 Introduction 2.1.1 Chapter Overview 2.2 Related Work 2.2.1 Natural Language Processing (NLP) 2.2.2 Literature and Graphs 2.2.3 Markov Chains and Metric Space 2.3 Definitions 2.3.1 Scripts 2.4 Graphs for Dramas 2.4.1 Frequency Graphs 2.5 Construction of the WW,AB,ABA Graphs 2.5.1 WW Graph 2.5.2 The AB Graph 2.5.3 The ABA Graph 2.5.4 ABA Subgraph of AB 2.5.5 Single Edge Changes in Social Networks 2.6 Transforming Literature Graphs 2.6.1 Markov Chains 2.6.2 Metric Space 2.6.3 From Frequency Graph G(V,E) to Metric Space (V,dis) 2.7 Applications of Frequency Graphs 2.8 Conclusion 2.9 Exercises 3 Partition in Social Network 3.1 Introduction 3.2 Partition and Conflict 3.2.1 Graph Partition 3.2.2 Partitions as Functions 3.2.3 Party Member Vectors and Functions 3.2.4 Conflict in Literature and Social Networks 3.2.5 Partition as Incidence Matrix 3.3 Related Work 3.4 Community Detection Algorithms 3.4.1 Vertex Moving Algorithm 3.4.2 Spectral Algorithm 3.4.3 Modularity Maximization 3.4.4 Edge Centrality Partition 3.4.5 Clique Percolation Method 3.4.6 Hierarchical Clustering 3.5 Experimenting with Community Detection Algorithms 3.6 Community Detection Algorithms and Literature Networks 3.7 Conflict Search Space 3.8 Conclusion 3.9 Exercises 4 Taking the Road Less Traveled: Decision Matrices 4.1 Introduction 4.2 Related Work 4.2.1 Option Analysis 4.3 Conflict Dynamics 4.3.1 Sequence of Partitions 4.3.2 Fixed Points and Conflict Dynamics 4.4 Example: Election in Gridland 4.4.1 Summary of Gridland Election 4.4.2 Community Detection Algorithms and Narrative 4.5 Infusing Logic into the Model: Decision Matrix 4.6 Decision Functions 4.7 Decision Matrix Example: Influence Functions 4.8 Conclusion 4.9 Exercises 5 Social Rationality and Networks 5.1 Introduction 5.2 Related Work: Social Rationality 5.3 Freedom of Interpretation and Anchors 5.3.1 Direction of Total Order 5.4 Utility Anchors 5.5 Rationality in Social Networks 5.6 Partition Functions 5.6.1 Personal Partition Function 5.7 Conflict Functions 5.7.1 Narrative Interpretation and Conflict Functions 5.7.2 Community Detection Algorithms and Conflict Functions 5.8 Rationality as Narrative 5.9 Conclusion 5.10 Exercises 6 Sun Tzu Says: Direct Attack 6.1 Introduction 6.2 Related Work: Voronoi Partitions 6.3 Direct Attack as Metric Space 6.3.1 Example: Euclidean Voronoi Partitions 6.4 Voronoi Option Analysisi 6.4.1 Voronoi: Optimization Description 6.4.2 Example: Voronoi War 6.4.3 Gridland Becomes Cycleland 6.4.4 Cycleland 6.4.5 Voronoi: Algorithmic Description 6.4.6 ``Speed is the Essence of War'' 6.5 Rationality of Voronoi Option Analysis 6.6 Voronoi Partition as a Greedy Algorithm 6.7 Conclusion 6.8 Exercises 7 Indirect Attack 7.1 Introduction 7.2 Related Work 7.3 Voting Option Analysis 7.3.1 Voting: Kirchhoff Description 7.3.2 Voting: Markov Chain Description 7.3.3 Voting Optimization Description: Divide and Conquer 7.3.4 Voting and Nas Equilibrium 7.3.5 Voting: Algorithmic Description 7.4 Solving the Voting System 7.5 Rationality of the Voting Algorithm 7.6 Conclusion 7.7 Exercises 8 1812: Social Networks Capture Napoleon 8.1 Introduction 8.2 Capturing Nodes in Consecutive Conflicts 8.3 Winning and Losing 8.3.1 Battle of Borodino (1812) 8.3.2 US Presidential Elections 8.4 Incorporating Narrative into War 8.4.1 Example 8.5 Party Power Base 8.6 Total War: Elimination of a Party 8.7 Conclusion 8.8 Exercises 9 The Search for Conflict 9.1 Introduction 9.2 Algorithm Complexity of Conflict 9.2.1 Computing Conflicts in Narratives 9.2.2 Measuring Conflict in Decision Matrices 9.3 Literary Analysis 9.4 Conclusion 9.5 Exercises 10 Ego Networks in Dramas 10.1 Introduction 10.2 Related Work 10.3 Definition of Ego Networks 10.4 Ego Networks in Dramas 10.5 Conclusion 10.6 Exercises Part II Evolution and Time in Literature Networks 11 Introduction to Evolving Social Networks 11.1 Introduction 11.2 Notation 11.2.1 Modeling Time 11.2.2 Modeling Space 11.3 Related Work 11.4 Evolving Social Networks: The Model 11.5 Evolving Social Networks: Example 11.5.1 Link Streams as Evolving Social Networks 11.5.2 Weighted Link Streams 11.6 From Performance Text to Link Stream 11.7 Link Streams with a Codomain of Matrices 11.8 Integration of Link Streams 11.8.1 Link Stream Integration over Graph Space 11.8.2 Differentiable 11.9 Sub-evolving Social Network 11.10 Conclusion 11.11 Exercises 12 Clocks 12.1 Introduction 12.2 Related Work 12.2.1 Subjective, Retrospective, and Prospective Time 12.3 The Relationship Between Prospective Clocks and Retrospective Clocks 12.4 General Clocks 12.5 Discrete Clocks 12.6 Continuous Clocks 12.6.1 Moving from Discrete Clocks to Continuous Clocks 12.7 Event Clocks and Weighted Clocks 12.8 Equivalent Clocks 12.9 Normalizing Clocks 12.10 Sub-graph Clocks 12.10.1 Dialog, or Edge, Clocks 12.10.2 Examples of Sub-graph Clocks 12.11 Link Streams and Clocks 12.12 Conclusion 12.13 Exercises 13 M-Diagrams 13.1 Introduction 13.2 Time Diagrams 13.3 M-Diagram Example: The Case of Felix Baumgartner 13.4 M-Diagrams for General Functions 13.5 Conclusion 13.6 Exercises 14 The Tale of Two Clocks 14.1 Introduction 14.2 Related Work 14.3 Framework of Two Clocks 14.3.1 Framework of Two Clocks in Performance Texts 14.4 Time Perception 14.5 Clocks 14.6 Comparing Clocks 14.6.1 Correlation Between Two Clocks 14.7 Single Clock Drift 14.8 The Gap Algorithm of Two Clocks 14.8.1 Comparing Different Clocks in Dramas 14.9 The Law of Two Clocks 14.10 Predicting Using the Clock Drift Algorithm 14.11 Conclusion 14.12 Exercises 15 Real Functions 15.1 Introduction 15.2 Related Work 15.3 Definitions 15.4 Normalized Functions and Correlation 15.5 Example: Degree Centrality 15.6 Degree Centrality in Dramas 15.7 Normalized Degree Centrality in Discrete Time 15.8 Normalized Degree Centrality in Continuous Time 15.9 Application to Dramas 15.9.1 Macbeth and Centrality Measures 15.9.2 The Godfather and Centrality Measures 15.10 Conclusion 15.11 Exercises 16 Evolving Social Network High Dimensions and Time Frames 16.1 Introduction 16.2 Related Work 16.3 High-Dimensional Evolving Social Network 16.4 High-Dimensional Real Function Spaces 16.5 Two-Dimensional Surfaces 16.5.1 The Three Witches in Macbeth 16.6 Examples in Dramas 16.6.1 Evolving Centrality in Death of a Salesman 16.6.2 Evolving Centrality in The Godfather 16.7 Conclusion 16.8 Exercises Part III Case Studies 17 Introduction to Case Studies 17.1 Introduction to Case Studies 18 Machine Narrative 18.1 Introduction 18.1.1 AI: Utopia or Dystopia? 18.2 Did the Author Ever Live? 18.3 Turing Machines 18.4 Turing Machines and Literature 18.4.1 Duality Between Machines and Narrative 18.4.2 The Judge and Interpretation 18.5 Definition of Narrative 18.5.1 Relationship Between M Functions 18.6 Drama Narrative 18.7 Example of a Drama Machine 18.7.1 Deterministic Caesar: Locus of Control Through the Lens of Julius Caesar 18.8 Conclusion 18.9 Exercises 19 Evolving Point of View 19.1 Introduction 19.2 Definition of Point of View 19.3 Methodology 19.4 Point of View 19.5 Point of View Examples 19.5.1 Dialogue Point of View 19.5.2 Egocentric Point of View 19.5.3 Gossip Point of View 19.6 Conclusion 19.7 Exercises 20 Search in Social Networks: The Science of Deduction 20.1 Introduction 20.2 Related Works 20.3 The Concept of Power Couples 20.4 Power Couple General Algorithm 20.5 Finding Power Couples Using a Space Approach 20.5.1 Simple Example 20.5.2 Finding Couples Using Dynamics 20.6 Case Study: Couples in Literature 20.6.1 Macbeth 20.6.2 Romeo and Juliet 20.7 Conclusion 20.8 Exercises 21 Evil in Social Networks 21.1 Introduction 21.2 Related Work 21.3 Evil as the Destruction of Social Fabric 21.4 Evil in Richard III 21.5 Representation of Evil in Dramas Viewed Through Space 21.6 Representation of Evil in Dramas Viewed Through Time 21.7 Conclusion 21.8 Exercises 22 Rise and Fall in Social Networks 22.1 Introduction 22.2 Related Work 22.3 Life and Death in Evolving Social Networks 22.4 Life and Death of Nodes 22.5 Life After Death, or An for An 22.5.1 Heaven and Hell 22.5.2 Macbeth Example 22.6 Universal Bounds on Degree Centrality 22.7 Literary Case Study: Julius Caesar 22.8 Conclusion 22.9 Exercises Appendix A Script Sources and Structure A.1 Introduction A.2 Scripts and .srt Files A.3 Performance Text Sources A.4 Conclusion Appendix B Mathematical Background for Literature Networks B.1 Introduction B.2 Notation Conventions B.3 Numbers and Sets B.3.1 Numbers B.3.2 Sets B.3.3 Multisets B.3.4 Vectors and Matrices B.3.5 Functions B.4 Graphs and Social Networks B.5 Graph Representation B.5.1 Transforming Networks and Matrices B.5.2 Metric Space B.5.3 Special Graphs B.5.4 Subgraphs and Neighborhoods B.5.5 Vertex Properties B.5.6 Centrality B.5.7 Cartesian Products and Grids Appendix C Introduction to Stochastic Processes C.1 Probability Space C.2 Random Variables C.2.1 Expectation, Variance, and Co-Variance C.2.2 Correlation C.3 Simple Random Walks: An Informal Description C.4 Markov Chains C.5 Network Centrality: PageRank C.6 Algorithms: Asymptotic Appendix D Turing Machines References Index