Syllabus

Course Meeting Times

Lectures: 1 session / week, 2 hours / session

Summary

Complex systems, such as the cell, cities or the economy, are formed by heterogeneous collections of components and interactions. During recent years the science of networks emerged as an alternative approach to analyze the structure and evolution of complex systems. In this course, we introduce the basic concepts and applications of network science for a general audience. The course will cover:

  • Basic network models;
  • A wide array of statistics used to characterize the structure and dynamics of networks;
  • Examples of naturally occurring networks in biology, technology, and social systems, including social networks and economic networks; and
  • Theories and applications of networks and complexity science that can be used to explain and understand the structure of the studied systems.

Evaluation

Students will be evaluated through homework, presentations, class participation and by the questions students ask the invited speakers.

ACTIVITIES PERCENTAGES
Homework 30%
Class project and presentation 60%
Participation 10%

Calendar

SES # TOPICS CONCEPTS COVERED KEY DATES
1 Introduction to Network Structure
  • Random Graphs
  • Small World Effect
  • Watts and Strogatz Model
  • Scale Free Networks
  • Barabási-Albert Model
  • Network Robustness and Fragility
  • Power-Laws
  • Epidemic Spreading Continued
  • Diffusion in and out of Networks
  
2 Qualifying Networks
  • Centrality Measures
  • Hierarchy
  • Assortativity/Degree Correlations
  • Modularity and Community Structure
  • Nestedness
  
3 Social Networks
  • Social networks
  
4 Visualizing Networks
  • Introduction to Cytoscape and Gephi
  
5 Networks, Complexity and Economic Development
  • Networks, Complexity and Economic Development
 Problem Set 1 due
6 Evolution and how it can help us understand our world
  • Evolution
  
7 Other Topics in Complexity Science
  • Chaos
  • The Lorenz Attractor
  • Tent and Logistic Maps
  • Self-Organized Criticality
  • Lyapunov Exponents
  • Scaling Laws
  
8 Topic to be determined based on progression of class   Problem Set 2 due
9 Topic to be determined based on progression of class (cont.)    
10 Final Presentations   Problem Set 3 due