Complex Systems 535/Physics 508, Fall 2009: 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.


In addition to reading assignments, 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 will take place on Thursday, October 22 from 10 till 11:30am; the final will be on Monday, December 21 from 10:30am till 12:30pm. Grade will be 35% on the homeworks, 30% on the mid-term, and 35% on the final.


Course-pack: There are two required course-packs for this course, one for the first half of the semester and one for the second half. Together they contain a complete copy of a new textbook on networks by Professor Newman that will be published by Oxford University Press next year. Copies are available from Dollar Bill Copying on Church St. Ask for CmplxSys 535/Physics 508, Prof. Newman, Bin 6064 (first course-pack) or Bin 6209 (second course-pack).

Books: A list of useful books is given below. None of them is required. However, if you want recommendations, I'd recommend for graph theory either Wilson (introductory) or West (more advanced), and for social network analysis either Scott or Wasserman & Faust. The Ahuja book is excellent if you're interested in the computer programming/algorithms side of things. Meyer is good if you need to brush up on your linear algebra.

Other web sites:

Problem sets:

Practice problems:

Here are some practice problems for the mid-term. Here are the solutions.


DateTopicReadingOn-line resourcesNotes
Tuesday, Sept. 8IntroductionChapter 1Information sheet
Thursday, Sept. 10Technological and social networksChapters 2 and 3
Tuesday, Sept. 15Information and biological networksChapters 4 and 5
Thursday, Sept. 17Mathematics of networks6.1-6.11 Homework 1Homework 1 handed out
Tuesday, Sept. 22Centrality7.1-7.7
Thursday, Sept. 24Transitivity, reciprocity, etc.7.8-7.13Homework 2 Homework 2 handed out
Tuesday, Sept. 29Observed structure of networksChapter 8
Thursday, Oct. 1Data structures and complexityChapter 9 Homework 3Homework 3 handed out
Tuesday, Oct. 6Shortest paths10.1-10.5
Thursday, Oct. 8Maximum flows and minimum cuts6.12 and 10.6 Homework 4 Homework 4 handed out
Tuesday, Oct. 13Matrix algorithms11.1-11.3
Thursday, Oct. 15Graph partitioning11.4-11.11No homework this week
Tuesday, Oct. 20No class Fall Break
Thursday, Oct. 22Mid-term examPractice problems, solutions In-class, usual time and place
Tuesday, Oct. 27Random graphs 1 12.1-12.5
Thursday, Oct. 29Random graphs 2 12.6-12.8Homework 5 Homework 5 handed out
Tuesday, Nov. 3Configuration models 1 13.1-13.4
Thursday, Nov. 5Configuration models 2 13.5-13.8 Homework 6Homework 6 handed out
Tuesday, Nov. 10Configuration models 3 13.9-13.11
Thursday, Nov. 12Generative models 1 14.1-14.2Homework 7 Homework 7 handed out
Tuesday, Nov. 17Generative models 2 14.3
Thursday, Nov. 19Generative models 3 14.4-14.5Homework 8 Homework 8 handed out, due Dec. 3
Tuesday, Nov. 24The small-world model 15.1
Thursday, Nov. 26No class Thanksgiving
Tuesday, Dec. 1Percolation Chapter 16
Thursday, Dec. 3Epidemics on networks 17.1-17.8Homework 9 Homework 9 handed out
Tuesday, Dec. 8Network search Chapter 19
Thursday, Dec. 10Review Review topics, Sample problemsLast class
Monday, Dec. 21Final Exam

Mark Newman