Complex Systems 535/Physics 508, Fall 2011: 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 is currently scheduled for October 20, but be aware that this date could change; the final will (definitely) be on Friday, December 16 from 4pm till 6pm. 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)

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:

Books on specific networky topics:

Problem sets:

Sample exams:


DateTopicReadingOn-line resourcesNotes
Tuesday, Sept. 6IntroductionChapter 1
Thursday, Sept. 8Technological and social networksChapters 2 and 3
Tuesday, Sept. 13Information and biological networksChapters 4 and 5
Thursday, Sept. 15Basic mathematics of networks6.1-6.11Homework 1 Homework 1 handed out
Tuesday, Sept. 20Centrality7.1-7.7
Thursday, Sept. 22Transitivity, reciprocity, assortativity7.8-7.13Homework 2 Homework 1 due, Homework 2 handed out
Tuesday, Sept. 27Component structure and the small-world effect8.1-8.2
Thursday, Sept. 29Degree distributions8.3-8.6Homework 3 Homework 2 due, Homework 3 handed out
Tuesday, Oct. 4Computer algorithms and complexityChapter 9
Thursday, Oct. 6Shortest paths10.1-10.5 Homework 4 Homework 3 due, Homework 4 handed out
Tuesday, Oct. 11Maximum flows and minimum cuts6.12 and 10.6
Thursday, Oct. 13Matrix algorithms and graph partitioningChapter 11Homework 4 due, no new homework this week
Tuesday, Oct. 18No class Fall Break
Thursday, Oct. 20Mid-term examIn-class, usual time and place
Tuesday, Oct. 25Random graphs 1 12.1-12.5
Thursday, Oct. 27Random graphs 2 12.6-12.8Homework 5 Homework 5 handed out
Tuesday, Nov. 1Configuration models 1 13.1-13.4
Thursday, Nov. 3Configuration models 2 13.5-13.8Homework 6 Homework 5 due, Homework 6 handed out
Tuesday, Nov. 8Configuration models 3 13.9-13.11
Thursday, Nov. 10Generative models 1 14.1-14.2Homework 7 Homework 6 due, Homework 7 handed out
Tuesday, Nov. 15Generative models 2 14.3
Thursday, Nov. 17Generative models 3 14.4-14.5Homework 8 Homework 7 due, Homework 8 handed out, due Dec. 1
Tuesday, Nov. 22The small-world model 15.1
Thursday, Nov. 24No class Thanksgiving
Tuesday, Nov. 29Percolation Chapter 16
Thursday, Dec. 1Epidemics on networks 17.1-17.8Homework 9 Homework 8 due, Homework 9 handed out
Tuesday, Dec. 6Network dynamics Chapter 18
Thursday, Dec. 8Network search Chapter 19Homework 9 due
Tuesday, Dec. 13Review
Friday, Dec. 16Final Exam Practice exam

Mark Newman