Complex Systems 535/Physics 508, Fall 2009: Network Theory

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Wednesdays 1:30-3:30pm
Email: [email protected]

Description:

This course will introduce and develop the mathematical theory of networks, particularly social and technological networks, with applications to network-driven phenomena in the Internet, search engines, network resilience, epidemiology, and many other areas.

Topics to be covered will include experimental studies of social networks, the world wide web, information and biological networks; methods and computer algorithms for the analysis and interpretation of network data; graph theory; models of networks including random graphs, preferential attachment models, and the small-world model; network dynamics.

Requirements

Students should have studied calculus and linear algebra before taking the course, and should in particular be comfortable with the solution of linear differential equations and with the calculation and properties of eigenvalues and eigenvectors of matrices. In addition, a moderate portion of the course, perhaps three weeks, will deal with computer methods for studying networks. Although students will not be required to write computer programs, some experience with computer programming will be a great help in understanding this part of the course.

Coursework

In addition to reading assignments, there will be weekly graded problem sets, consisting both of theory questions and of problems demonstrating applications of theory to example networks. There will be one mid-term and a final. The mid-term will take place on Thursday, October 22 from 10 till 11:30am; the final will be on Monday, December 21 from 10:30am till 12:30pm. Grade will be 35% on the homeworks, 30% on the mid-term, and 35% on the final.

Resources

Course-pack: There are two required course-packs for this course, one for the first half of the semester and one for the second half. Together they contain a complete copy of a new textbook on networks by Professor Newman that will be published by Oxford University Press next year. Copies are available from Dollar Bill Copying on Church St. Ask for CmplxSys 535/Physics 508, Prof. Newman, Bin 6064 (first course-pack) or Bin 6209 (second course-pack).

Books: A list of useful books is given below. None of them is required. However, if you want recommendations, I'd recommend for graph theory either Wilson (introductory) or West (more advanced), and for social network analysis either Scott or Wasserman & Faust. The Ahuja book is excellent if you're interested in the computer programming/algorithms side of things. Meyer is good if you need to brush up on your linear algebra.

• R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications, Prentice Hall, Upper Saddle River, NJ (1993)
• A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge (2008)
• S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks, Oxford University Press, Oxford (2003)
• A. Degenne and M. Forse, Introducing Social Networks, Sage, London (1999)
• F. Harary, Graph Theory, Perseus, Cambridge, MA (1995)
• M. O. Jackson, Social and Economic Networks, Princeton University Press, Princeton, NJ (2008)
• C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, PA (2000)
• J. Scott, Social Network Analysis: A Handbook, 2nd edition, Sage, London (2000)
• S. Wasserman and K. Faust, Social Network Analysis, Cambridge University Press, Cambridge (1994)
• D. J. Watts, Six Degrees: The Science of a Connected Age, Norton, New York (2003)
• D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, NJ (1996)
• R. J. Wilson, Introduction to Graph Theory, 4th edition, Addison-Wesley, Reading, MA (1997)

• Physics preprints
• Pajek network software for Windows (also runs on Linux or Mac using Wine or SoftPC)
• GraphViz network software for any platform (Windows, Linux, Mac)
• Yed network software for any platform (Windows, Linux, Mac)

Problem sets:

• Homework 1 - Fundamental mathematics of networks
• Homework 2 - Centrality measures
• Homework 3 - Degree distributions, clustering, etc.
• Homework 4 - Computer algorithms
• Homework 5 - Random graphs
• Homework 6 - The configuration model
• Homework 7 - Configuration models and growing networks
• Homework 8 - Growing networks and the small-world model
• Homework 9 - Percolation and epidemics

Practice problems:

Syllabus