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.
Author(s): Zvi Lotker
Edition: 1
Publisher: Springer
Year: 2021
Language: English
Commentary: Vector PDF
Pages: 414
City: New York, NY
Tags: Machine Learning; Probabilistic Models; Natural Language Processing; Psychology; Linguistics; Sentiment Analysis; Social Networks; Graph Theory; Graph Algorithms; Markov Models; Algorithms; Literary Theory; Narrative Model; Conflict Function
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
