Complex Systems 535/Physics 508, Fall 2010: Network Theory

Time: Tuesday and Thursday, 10-11:30am
Room: 455 Dennison

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Wednesdays 1:30-3:30pm


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.


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.


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 in class on Thursday, October 21; the final will be on Friday, December 17 from 1:30pm till 3:30pm. Grade will be 35% on the homeworks, 30% on the mid-term, and 35% on the final.

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.


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

Other books: A list of other 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.

Problem sets:

Practice problems:

Here are some practice problems for the mid-term. Here are the solutions.


DateTopicReadingOn-line resourcesNotes
Tuesday, Sept. 7IntroductionChapter 1
Thursday, Sept. 9Technological and social networksChapters 2 and 3
Tuesday, Sept. 14Information and biological networksChapters 4 and 5
Thursday, Sept. 16Mathematics of networks6.1-6.11Homework 1 Homework 1 handed out
Tuesday, Sept. 21Centrality7.1-7.7
Thursday, Sept. 23Transitivity, reciprocity, etc.7.8-7.13Homework 2 Homework 1 due, Homework 2 handed out
Tuesday, Sept. 28Component structure and the small-world effect8.1-8.2
Thursday, Sept. 30Degree distributions8.3-8.6Homework 3 Homework 2 due, Homework 3 handed out
Tuesday, Oct. 5Data structures and complexityChapter 9
Thursday, Oct. 7Shortest paths10.1-10.5 Homework 4 Homework 3 due, Homework 4 handed out
Tuesday, Oct. 12Maximum flows and minimum cuts6.12 and 10.6
Thursday, Oct. 14Matrix algorithms and graph partitioningChapter 11Homework 4 due, no new homework this week
Tuesday, Oct. 19No class Fall Break
Thursday, Oct. 21Mid-term examPractice problems, solutions In-class, usual time and place
Tuesday, Oct. 26Random graphs 1 12.1-12.5
Thursday, Oct. 28Random graphs 2 12.6-12.8Homework 5 Homework 5 handed out
Tuesday, Nov. 2Configuration models 1 13.1-13.4
Thursday, Nov. 4Configuration models 2 13.5-13.8Homework 6 Homework 5 due, Homework 6 handed out
Tuesday, Nov. 9Configuration models 3 13.9-13.11
Thursday, Nov. 11Generative models 1 14.1-14.2Homework 7 Homework 6 due, Homework 7 handed out
Tuesday, Nov. 16Generative models 2 14.3
Thursday, Nov. 18Generative models 3 14.4-14.5Homework 8 Homework 7 due, Homework 8 handed out, due Dec. 2
Tuesday, Nov. 23The small-world model 15.1
Thursday, Nov. 25No class Thanksgiving
Tuesday, Nov. 30Percolation Chapter 16
Thursday, Dec. 2Epidemics on networks 17.1-17.8Homework 9 Homework 8 due, Homework 9 handed out
Tuesday, Dec. 7Network search Chapter 19
Thursday, Dec. 9Review Homework 9 due
Friday, Dec. 17Final Exam

Mark Newman