The course begins with an overview of basic backgrounds. We will then cover network properties, strong and weak ties, homophily, positive and negative relationships, games on networks, evolutionary game theory, traffic on networks, auctions, and other topics. One goal of the course is to identify potential research questions for students. By the end of this course, students will have: (1) Broad understanding of social network analysis. (2) Knowledge and tools to analyze social and economic networks. (3) Fundamental understanding of modeling group behavior. (4) The ability to understand research papers in the field of social networks.

The course provides an overview of models and techniques for analyzing social networks and group behavior. The course is meant for undergraduate and graduate students in College of Social Sciences with a good mastery of math/statistics who are interested both in the theoretical study of networks and in their application to political, social and economic phenomena.


Week 1: Course Overview
Week 2: Graphs
a. Basic Definitions
b. Paths and Connectivity
c. Distance and Breadth-First Search
d. Network Datasets: An Overview
Week 3: Strong and Weak Ties
a. Triadic Closure
b. The Strength of Weak Ties
c. Tie Strength and Network Structure in Large-Scale Data
d. Tie Strength, Social Media, and Passive Engagement
e. Closure, Structural Holes, and Social Capital
Week 4: Networks in Their Surrounding Contexts
a. Homophily
b. Mechanisms Underlying Homophily: Selection and Social Influence
c. Affiliation
d. Tracking Link Formation in On-Line Data
e. A Spatial Model of Segregation
Week 5: Positive and Negative Relationships
a. Structural Balance
b. Characterizing the Structure of Balanced Networks
c. Applications of Structural Balance
d. A Weaker Form of Structural Balance
Week 6: No Class
Week 7: Games
a. What is a Game?
b. Reasoning about Behavior in a Game
c. Best Responses and Dominant Strategies
d. Nash Equilibrium
e. Multiple Equilibria: Coordination Games
f. Multiple Equilibria: The Hawk-Dove Game
g. Mixed Strategies
h. Mixed Strategies: Examples and Empirical Analysis
i. Pareto-Optimality and Social Optimality
Week 8: Evolutionary Game Theory
a. Fitness as a Result of Interaction
b. Evolutionarily Stable Strategies
c. A General Description of Evolutionarily Stable Strategies
d. Evolutionarily Stable Mixed Strategies
Week 9: Midterm Exam
Week 10: Modeling Network Traffic using Game Theory
a. Traffic at Equilibrium
b. Braess's Paradox
Week 11: Auctions
a. Types of Auctions
b. When are Auctions Appropriate?
c. Relationships between Different Auction Formats
d. Second-Price Auctions
e. First-Price Auctions and Other Formats
f. Common Values and The Winner's Curse
Week 12: Information Cascades
a. Following the Crowd
b. A Simple Herding Experiment
c. Bayes' Rule: A Model of Decision-Making Under Uncertainty
d. Bayes' Rule in the Herding Experiment
e. A Simple, General Cascade Model
f. Sequential Decision-Making and Cascades
Week 13: Network Effects
a. The Economy Without Network Effects
b. The Economy with Network Effects
c. Stability, Instability, and Tipping Points
d. A Dynamic View of the Market
e. Industries with Network Goods
f. Mixing Individual Effects with Population-Level Effects
Week 14: Power Laws and Rich-Get-Richer Phenomena
a. Power Laws
b. Rich-Get-Richer Models
c. The Unpredictability of Rich-Get-Richer Effects
d. The Long Tail
e. The Effect of Search Tools and Recommendation Systems
Week 15: Cascading Behavior in Networks Power Laws
a. Diffusion in Networks
b. Modeling Diffusion through a Network
c. Cascades and Clusters
d. Diffusion, Thresholds, and the Role of Weak Ties
e. Extensions of the Basic Cascade Model
f. Knowledge, Thresholds, and Collective Action
Week 16: The Small-World Phenomenon
a. Six Degrees of Separation
b. Structure and Randomness
c. Decentralized Search
d. Empirical Analysis and Generalized Models
e. Core-Periphery Structures and Difficulties in Decentralized Search
Week 17: Epidemics
a. Diseases and the Networks that Transmit Them
b. Branching Processes
c. The SIR Epidemic Model
d. The SIS Epidemic Model
e. Synchronization
f. Transient Contacts and the Dangers of Concurrency
g. Genealogy, Genetic Inheritance, and Mitochondrial Eve
Week 18: Final Exam