Complex Systems 535/Physics 508, Fall 2013: 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 and preferential attachment models; spectral methods and random matrix theory; maximum likelihood methods; percolation theory; network search.


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.


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 24, November 5, 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.


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. 3IntroductionChapter 1
Thursday, Sept. 5Technological and social networksChapters 2 and 3
Tuesday, Sept. 10Information and biological networksChapters 4 and 5
Thursday, Sept. 12Basic mathematics of networks6.1-6.11Homework 1 Homework 1 handed out
Tuesday, Sept. 17Centrality, transitivity, assortativityChapter 7
Thursday, Sept. 19Network structure and degree distributions8.1-8.6 Homework 1 due, no new homework this week
Tuesday, Sept. 24Midterm 1In class, usual time and place
Thursday, Sept. 26Computer algorithmsChapter 9Homework 2Homework 2 handed out
Tuesday, Oct. 1Shortest paths10.1-10.4
Thursday, Oct. 3Matrix algorithms and graph partitioningChapter 11Homework 3Homework 2 due, Homework 3 handed out
Tuesday, Oct. 8Random graphs 112.1-12.5
Thursday, Oct. 10Random graphs 212.6-12.8Homework 4Homework 3 due, Homework 4 handed out, due Oct. 24
Tuesday, Oct. 15No class Fall Break
Thursday, Oct. 17Network spectra No new homework this week
Tuesday, Oct. 22Random matrix theory
Thursday, Oct. 24Configuration models 1 13.1-13.4Homework 5Homework 4 due, Homework 5 handed out
Tuesday, Oct. 29Configuration models 2 13.5-13.8
Thursday, Oct. 31Configuration models 3 13.9-13.11No new homework this week
Tuesday, Nov. 5Midterm 2 In class, usual time and place. Homework 5 due.
Thursday, Nov. 7Maximum likelihood methods Homework 6Homework 6 handed out
Tuesday, Nov. 12No class
Thursday, Nov. 14The expectation-maximization methodHomework 6 due, no new homework this week
Tuesday, Nov. 19No class
Thursday, Nov. 21Generative models 1 14.1-14.2Homework 7Homework 7 handed out, due Dec. 5
Tuesday, Nov. 26Generative models 2 14.3-14.5
Thursday, Nov. 28No class Thanksgiving
Tuesday, Dec. 3Percolation Chapter 16
Thursday, Dec. 5Epidemics on networks 17.1-17.8Homework 7 due
Tuesday, Dec. 10Midterm 3 In class, usual time and place

Mark Newman