Complex Systems 535/Physics 508, Fall 2012: 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 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; 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 analyzing 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 of questions on both theory and applications. There will be two mid-term exams but no final. The mid-terms will be in class at the usual time on October 18 and December 11.

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:


DateTopicReadingOn-line resourcesNotes
Tuesday, Sept. 4IntroductionChapter 1
Thursday, Sept. 6Technological and social networksChapters 2 and 3
Tuesday, Sept. 11Information and biological networksChapters 4 and 5
Thursday, Sept. 13Basic mathematics of networks6.1-6.11 Homework 1Homework 1 handed out
Tuesday, Sept. 18Centrality7.1-7.7
Thursday, Sept. 20Transitivity, reciprocity, assortativity7.8-7.13 Homework 2 Homework 1 due, Homework 2 handed out
Tuesday, Sept. 25Network structure and degree distributions8.1-8.6
Thursday, Sept. 27Computer algorithms and complexityChapter 9Homework 3Homework 2 due, Homework 3 handed out
Tuesday, Oct. 2Shortest paths10.1-10.4
Thursday, Oct. 4Maximum flows and minimum cuts6.12 and 10.5Homework 4, Data fileHomework 3 due, Homework 4 handed out
Tuesday, Oct. 9Matrix algorithms and graph partitioningChapter 11
Thursday, Oct. 11Maximum likelihood methodsHomework 4 due, no new homework this week
Tuesday, Oct. 16No class Fall Break
Thursday, Oct. 18Mid-term 1 In class, usual time and place
Tuesday, Oct. 23Random graphs 1 12.1-12.5
Thursday, Oct. 25Random graphs 2 12.6-12.8Homework 5 Homework 5 handed out
Tuesday, Oct. 30Configuration models 1 13.1-13.4
Thursday, Nov. 1Configuration models 2 13.5-13.8Homework 6 Homework 5 due, Homework 6 handed out
Tuesday, Nov. 6Configuration models 3 13.9-13.11
Thursday, Nov. 8Network spectra Homework 7 Homework 6 due, Homework 7 handed out
Tuesday, Nov. 13Generative models 1 14.1-14.2
Thursday, Nov. 15Generative models 2 14.3Homework 8 Homework 7 due, Homework 8 handed out, due Nov. 29
Tuesday, Nov. 20Generative models 3 14.4-14.5
Thursday, Nov. 22No class Thanksgiving
Tuesday, Nov. 27Percolation Chapter 16
Thursday, Nov. 29Epidemics on networks 17.1-17.8Homework 9 Homework 8 due, Homework 9 handed out
Tuesday, Dec. 4Network dynamics Chapter 18
Thursday, Dec. 6Network search Chapter 19Homework 9 due
Tuesday, Dec. 11Mid-term 2 In class, usual time and place

Mark Newman