Social Networks:


Professor B. Mishra
Teaching Assistants:
XingYang Chen [ email: ] and
Raphael Sofaer [ email: ]

Office Hours: By appt.
Office Phone: 212.998.3464
Email Address:

Day and Time:
Wednesday, 5:00-6:50pm EST, WWH 202.

Credits for Course:

Mathematical Maturity, Programming and Algorithms

Grading Policy:
Quiz: 55 %; Project: 35 %; Final Exam: 10 %

Social Networks is a specific example of many forms of networks that have become ubiquitous in our modern society. The World Wide Web enables information flows among vast number of humans; facebook, orkut, friendster, diaspora, etc. connect small groups of friends; amazon, ebay, etc. provide opportunities for trading, etc. These networks determine our information, influence our opinions, and shape our political attitudes.

They also link us, often through important but weak ties, to other humans. Their origin is biological: going back to quorum-sensing, swarming, flocking, social grooming, gossip, etc. Yet, as we have connected our social networks to traditional human institutions (markets, justice systems, education, etc.) through new technologies, the underlying biology has become obscured, but not dormant.

Economic markets also look much more like networks than anonymous marketplaces. Firms interact with the suppliers and customers in a Web-like supply chains. Systemic risk in financial markets often results from the counterparty risks created within this financial network.

This course will introduce the tools for the study of networks. It will show how certain common principles permeate the functioning of these diverse networks: e.g., issues related to robustness, fragility, and interlinkages etc.

(1) Introduction to networks (Social, Economic and Communication)

(2) Biology of Social Networks

(3) Graph theory and social networks

Directed and undirected graphs, paths, cycles, diameter, clustering, bipartite graphs. Applications: the web as a directed graph, homophily.

(4) Random graph models

Review of branching processes, Erdos-Renyi graphs, degree distributions, 0-1 Laws, connectedness, and giant component. Applications: tipping, six degrees of separation, and disease transmissions.

(5) Preferential attachment, power laws, and small worlds

Preferential attachment, degree distributions, generalized random graphs, and clustering. Applications: firm size distributions, link analysis and web search, PageRank, decentralized search, and navigation.

(6) Game theory

Games, strategies, payoffs, extensive and normal forms, and Nash equilibrium. Applications: tragedy of the commons and coordination games.

(7) Communication and Signaling

Evolution of Languages in Network, Decoding. Applications: Language of Twitter.

(8) Decisions in groups

Decision making in organizations and societies, social choice, Condorcet jury theorem, and political economy. Application: committee decisions.

(9) Macro-Economic Models and Supply-Chains

(9) Case Studies:

Facebook, ATTAP, Twitter, Wikileaks, Bit-coins, Arab Spring, Occupy Wallstreet

Required Text(s):

Recommended Text(s):

Midterm Date:
No Midterm.
Final Date:
Class Project.
Class Presentation.

Bud Mishra
September 1 2003