Complex Systems 535/Physics 508, Fall 2014: Network Theory

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Tuesday 1:30-3:30pm
Email: mejn@umich.edu

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 and preferential attachment models; spectral methods and random matrix theory; maximum likelihood methods; percolation theory; network search.

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 two weeks, will deal with computer methods for analyzing networks. Some experience with computer programming will be a great help in understanding this part of the course.

Coursework

There will be weekly graded problem sets, consisting of questions on both theory and applications. There will be three midterm exams but no final. The midterms will be in class at the usual time on September 29, November 3, and December 10.

There will be reading assignments for each lecture. The assignments are listed on the schedule below. Students are expected to do the reading for each lecture in a timely manner.

Books

Textbook (required): Networks: An Introduction, M. E. J. Newman, Oxford University Press, Oxford (2010)

In addition to this required text, a list of other useful books is given below. None of them is required, but you may find them useful if you want a second opinion or more detail on certain topics.

General books on networks:

• Reuven Cohen and Shlomo Havlin, Complex Networks: Structure, Robustness and Function, Cambridge University Press, Cambridge (2010). Quite a short book, but it covers most of the topics of the course, at least to some extent, and some others that are not in the book by Newman.
• S. N. Dorogovtsev, Lectures on Complex Networks, Oxford University Press, Oxford (2010). Very short – genuinely a set of lecture notes, rather than a full text.

Books on specific networky topics:

• 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. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge (2008)
• G. Caldarelli, Scale-Free Networks: Complex Webs in Nature and Technology, Oxford University Press, Oxford (2007)
• 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)
• D. Easley and J. Kleinberg, Networks, Crowds, and Markets, Cambridge University Press, Cambridge (2010)
• 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)
• M. E. J. Newman, A.-L. Barabasi, and D. J. Watts, The Structure and Dynamics of Networks, Princeton University Press (2006)
• R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet, Cambridge University Press, Cambridge (2007)
• 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)

Problem sets:

• Homework 1 - Mathematics of networks
• Homework 2 - Measures and metrics
• Homework 3 - Random graphs
• Homework 4 - The configuration model
• Homework 5 - Growing networks
• Homework 6 - Community structure and inference
• Homework 7 - EM algorithm and modularity

Syllabus

Date	Topic	Reading	On-line resources	Notes
Wednesday, Sept. 3	Introduction	Chapter 1	Info sheet
Monday, Sept. 8	Classes of networks	Chapters 2 through 5
Wednesday, Sept. 10	Basic mathematics of networks	6.1-6.11	Homework 1, Data set	Homework 1 handed out
Monday, Sept. 15	Centrality, transitivity, assortativity	Chapter 7
Wednesday, Sept. 17	Network structure and degree distributions	8.1-8.6	Homework 2, Data set	Homework 1 due, Homework 2 handed out
Monday, Sept. 22	Computer algorithms 1	Chapter 9
Wednesday, Sept. 24	Computer algorithms 2	10.1-10.4		Homework 2 due, no new homework this week
Monday, Sept. 29	Midterm 1			In class, usual time and place
Wednesday, Oct. 1	Random graphs 1	12.1-12.5	Homework 3	Homework 3 handed out, due Oct. 15
Monday, Oct. 6	No class
Wednesday, Oct. 8	Random graphs 2	12.6-12.8
Monday, Oct. 13	No class			Fall Break
Wednesday, Oct. 15	Configuration models 1	13.1-13.4	Homework 4	Homework 3 due, Homework 4 handed out
Monday, Oct. 20	Configuration models 2	13.5-13.8
Wednesday, Oct. 22	Configuration models 3	13.9-13.11	Homework 5	Homework 4 due, Homework 5 handed out
Monday, Oct. 27	Generative models 1	14.1-14.2
Wednesday, Oct. 29	Generative models 2	14.3-14.5		Homework 5 due, no new homework this week
Monday, Nov. 3	Midterm 2			In class, usual time and place
Wednesday, Nov. 5	Partitioning and community structure	11.2-11.8	Homework 6	Homework 6 handed out
Monday, Nov. 10	Maximum likelihood methods
Wednesday, Nov. 12	The expectation-maximization method			Homework 6 due, no new homework this week
Monday, Nov. 17	Spectral methods
Wednesday, Nov. 19	Random matrix theory 1		Homework 7, Data set	Homework 7 handed out, due Dec. 3
Monday, Nov. 24	Random matrix theory 2
Wednesday, Nov. 26	No class			Thanksgiving
Monday, Dec. 1	Percolation	Chapter 16
Wednesday, Dec. 3	Epidemics on networks	17.1-17.8		Homework 7 due
Monday, Dec. 8	Network search	Chapter 19
Wednesday, Dec. 10	Midterm 3			In class, usual time and place