Room: 4404 Randall Lab

Instructor: Mark Newman

Office: 277 West Hall

Office hours: Wednesdays 1:30-3:30pm

Email: mejn@umich.edu

Grader: Juyong Park

Office: 272 West Hall

Email: juyongp@umich.edu

This course will introduce and develop the mathematical theory of networks, particularly social and technological networks, with applications to important network-driven phenomena in epidemiology of human infections and computer viruses, the Internet, network resilience, web search engines, and many others.

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; computer simulation methods; network dynamics.

A syllabus for the course can be found here. The details may change, but this is reasonably accurate.

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.

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 be a take-home exam handed out on the Tuesday of the week after Winter break and due in two days later. The final will be on Wednesday, April 27 from 4pm till 6pm. Grade will be 40% on the homeworks, 25% on the mid-term, and 35% on the final.

- Homework 1 - Network analysis exercise. The data for the exercise are here.
- Homework 2 - Graph theory
- Homework 3 - Graph theory and network analysis
- Homework 4 - More network analysis. The data for the Chesapeake Bay food web are here and the degree sequence for the Little Rock Lake web is here.
- Homework 5 - Algorithms. The data for the karate club network are here.
- Homework 6 - Clustering. The data for the small network are here and for the "southern women" network here.
- Homework 7 - Generating functions
- Homework 8 - Random graphs
- Homework 9 - Growing graphs and the small-world model

There is **no set text** for this course because no one has written one
yet. But there is a course-pack as described below, there will be handouts
in class, and we may read some research papers that address particular
topics during the course. There are also a number of books that cover
parts of the material quite well.

**Course-pack:** The course-pack contains a copy of the review article
The structure and function of complex networks,
M. E. J. Newman, *SIAM Review* **45**, 167-256 (2003). Copies of
the course-pack are available from Howard Oishi in the Complex Systems
office (4485 Randall) for $3, or you are welcome to simply download the
article and print it yourself.

**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) - 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) - 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)

- Computer Networks, Jamin (Michigan)
- Information Retrieval, Radev (Michigan)
- The Structure of Information Networks, Kleinberg (Cornell)
- Networks and Complexity in Social Systems, Watts (Columbia)
- Scaling in Networks, Lazar (Columbia)
- Complex Human Networks Reading Group, Pentland, Clarkson, Choudhury (MIT)
- Information Retrieval, Discovery, and Delivery, LaPaugh (Princeton)
- Recommender Systems, Ramakrishnan (Virginia Tech)
- Networks and Complexity, White (UC Irvine)
- Large Scale Networked Systems, Foster (Chicago)
- Scaling, Power Laws, and Small World Phenomena in Networks, Towsley (U. Mass.)
- Networks, Boudourides (University of Patras, Greece)

- 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)- Social networks information

Mark Newman