Complex Systems 535/Physics 508, Fall 2014: Network Theory

Time: Monday and Wednesday, 1-2:30pm
Room: 2218 School of Education Building

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Tuesday 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 29, November 3, 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
Wednesday, Sept. 3IntroductionChapter 1Info sheet
Monday, Sept. 8Classes of networksChapters 2 through 5
Wednesday, Sept. 10Basic mathematics of networks6.1-6.11Homework 1, Data setHomework 1 handed out
Monday, Sept. 15Centrality, transitivity, assortativityChapter 7
Wednesday, Sept. 17Network structure and degree distributions8.1-8.6Homework 2, Data setHomework 1 due, Homework 2 handed out
Monday, Sept. 22Computer algorithms 1Chapter 9
Wednesday, Sept. 24Computer algorithms 210.1-10.4Homework 2 due, no new homework this week
Monday, Sept. 29Midterm 1In class, usual time and place
Wednesday, Oct. 1Random graphs 112.1-12.5Homework 3Homework 3 handed out, due Oct. 15
Monday, Oct. 6No class
Wednesday, Oct. 8Random graphs 212.6-12.8
Monday, Oct. 13No classFall Break
Wednesday, Oct. 15Configuration models 113.1-13.4Homework 4Homework 3 due, Homework 4 handed out
Monday, Oct. 20Configuration models 213.5-13.8
Wednesday, Oct. 22Configuration models 313.9-13.11Homework 5Homework 4 due, Homework 5 handed out
Monday, Oct. 27Generative models 114.1-14.2
Wednesday, Oct. 29Generative models 214.3-14.5Homework 5 due, no new homework this week
Monday, Nov. 3Midterm 2In class, usual time and place
Wednesday, Nov. 5Partitioning and community structure11.2-11.8Homework 6Homework 6 handed out
Monday, Nov. 10Maximum likelihood methods
Wednesday, Nov. 12The expectation-maximization methodHomework 6 due, no new homework this week
Monday, Nov. 17Spectral methods
Wednesday, Nov. 19Random matrix theory 1Homework 7, Data setHomework 7 handed out, due Dec. 3
Monday, Nov. 24Random matrix theory 2
Wednesday, Nov. 26No classThanksgiving
Monday, Dec. 1PercolationChapter 16
Wednesday, Dec. 3Epidemics on networks17.1-17.8Homework 7 due
Monday, Dec. 8Network searchChapter 19
Wednesday, Dec. 10Midterm 3In class, usual time and place

Mark Newman