Lecture notes 1–12 are adapted from the 2009 version of this course by Prof. Daron Acemoglu and Prof. Asu Ozdaglar and from the 2017 version of the course as taught by Prof. Shah.
| Ses # | Topics | Lecture Notes | Recitation Notes |
|---|---|---|---|
| 1 | Introduction to Social, Economic, and Technological Networks | Lecture 1 Slides (PDF - 2.6MB) | |
| 2–3 |
Network Representations, Measures, and Metrics
Directed and undirected graphs, adjacency matrix. Paths, cycles, connectivity, components. Trees, rings, stars, bipartite graphs, hyper graphs. Centrality measures (degree, closeness, betweenness), clustering, structural balance, homophily, and assortative mixing. Applications: Structural properties of Facebook graph. |
Lectures 2 & 3 Slides (PDF) | Recitation 1 (not available to OCW users) |
| 4–6 |
Linear Dynamical Systems, Markov Chains, Centralities
Discrete-time, linear time-invariant systems with constant inputs. Eigenvalue decomposition. Convergence to equilibrium. Lyapunov function. Positive linear systems, Markov chains, and Perron-Frobenius. Random walk on graph. Eigen centrality. Katz centrality. Page rank. Applications: Web search. |
Lectures 4, 5, & 6 Slides (PDF) | Recitations 2 & 3 (not available to OCW users) |
| 7 |
Dynamics Over Graph: Spread of Information and Distributed Computation
Algebraic properties of graphs, Cheeger's inequality, information spread and consensus. Applications: social agreement, synchronization, distributed optimization. |
Lecture 7 Slides (PDF) | Recitation 4 (not available to OCW users) |
| 8 |
Graph Decomposition and Clustering
Decomposing networks into clusters. Modularity. Spectral clustering and connectivity. |
Lecture 8 Slides (PDF) | |
| 9–11 |
Random Graph Models
Erdos-Renyi graphs. Review of branching processes. Degree distribution, phase transition, connectedness, giant component. Applications: tipping, six degrees of separation, disease transmissions. |
Recitations 5 & 6 (not available to OCW users) | |
| 12 |
Generative Graph Models
Preferential attachment: rich get richer phenomena, power laws. Small world models: clustering and path lengths. Applications: Internet topology, Facebook and Twitter degree distributions, firm size distributions. |
Lecture 12 Slides (PDF) | |
| 13–14 |
Introduction to Game Theory
Games, pure and mixed strategies, payoffs, Nash equilibrium, Bayesian games. Applications: tragedy of the commons, peer effects, auctions. |
Recitation 7 Notes | |
| 15 | Traffic Flow and Congestion Games | Lecture 15 Slides (PDF) | |
| 16 |
Network Effects (I)
Negative externalities, congestion, Braess' paradox, routing. Application: pricing traffic. |
Lecture 16 Slides (PDF) | Recitation 8 Notes |
| 17 |
Network Effects (II)
Key players and the social multiplier. Applications: criminal networks, public good provision, oligopoly. |
Lecture 17 Slides (PDF) | Recitation 9 Notes |
| 18 |
Networked Markets
Matching markets, markets with intermediaries, platforms. Applications: clearinghouses, ad exchanges, labor markets. |
Lecture 18 Slides (PDF) | |
| 19 |
Repeated Games, Cooperation, and Strategic Network Formation
Stable networks, Nash networks, efficient networks. Applications: co-authorship, R&D networks. |
Lecture 19 Slides (PDF) | Recitation 10 Notes |
| 20–21 |
Diffusion Models and Contagion
Positive externalities, strategic complements, coordination games, tipping, lock in, path dependence. Applications: diffusion of innovation. |
Rectation 11 Notes | |
| 22–24 |
Games with Incomplete Information and Introduction to Social Learning, Herding, and Informational Cascades
Rule of thumb and Bayesian learning, social influence, benefits of copying, herd behavior, informational cascades. Applications: consumer behavior, financial markets. |
Recitation 12 Notes |