Complex Systems 535/Physics 508, Fall 2015: Network Theory

Time: Tuesday and Thursday, 10-11:30am
Room: 1060 East Hall

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Monday 2-4pm

Quick links:


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 October 13, November 10, 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. 8IntroductionChapter 1Info sheet
Thursday, Sept. 10Technological and social networksChapters 2 and 3
Tuesday, Sept. 15Information networks and biological networksChapters 4 and 5Homework 1Homework 1 handed out
Thursday, Sept. 17Basic mathematics of networks6.1-6.11
Tuesday, Sept. 22Centrality, transitivity, assortativityChapter 7Homework 2Homework 1 due, Homework 2 handed out
Thursday, Sept. 24Network structure and degree distributions8.1-8.6
Tuesday, Sept. 29Computer algorithms 1Chapter 9Homework 3, Network data, Internet dataHomework 2 due, Homework 3 handed out
Thursday, Oct. 1Computer algorithms 210.1-10.4
Tuesday, Oct. 6Random graphs 112.1-12.5Homework 3 due, no new homework this week
Thursday, Oct. 8Random graphs 212.6-12.8
Tuesday Oct. 13Midterm 1Homework 4Homework 4 handed out, due Tuesday, Oct. 27
Thursday, Oct. 15Configuration models 113.1-13.4
Tuesday, Oct. 20No classFall Break
Thursday, Oct. 22Configuration models 213.5-13.8
Tuesday, Oct. 27Configuration models 313.9-13.11Homework 5Homework 4 due, Homework 5 handed out
Thursday, Oct. 29Generative models 114.1-14.2
Tuesday, Nov. 3Generative models 214.3-14.5Homework 5 due, no new homework this week
Thursday, Nov. 5Community structure11.2-11.6
Tuesday, Nov. 10Midterm 2Homework 6Homework 6 handed out
Thursday, Nov. 12Spectral methods11.7, 11.8
Tuesday, Nov. 17Maximum likelihood methods
Thursday, Nov. 19The expectation-maximization methodHomework 7, Blog network dataHomework 6 due, Homework 7 handed out
Tuesday, Nov. 24Belief propagation and detectability
Thursday, Nov. 26No classThanksgiving
Tuesday, Dec. 1PercolationChapter 16Homework 8Homework 7 due, Homework 8 handed out
Thursday, Dec. 3Epidemics on networks17.1-17.8
Tuesday, Dec. 8Network searchChapter 19Homework 8 due
Thursday, Dec. 10Midterm 3In class, usual time and place

Mark Newman