Complex Systems 535/Physics 508, Fall 2017: Network Theory

Time: Tuesday and Thursday, 10-11:30am
Room: 1028 Dana

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Monday 2-4pm
Email: mejn@umich.edu


Quick links:


Description:

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; community structure; percolation theory; network search.

Requirements

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.

Coursework

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 19, November 16, and December 12.

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.

Course packs and books

Course packs (required): There is no textbook for this course but there are two course packs. The first covers the first part of the semester up to the first midterm exam; the second covers the remainder of the semester. Both are available now from Dollar Bill Copying on Church Street. Ask for CMPLXSYS 535, Bin #6081 (course pack 1) and Bin #6118 (course pack 2).

In addition to the course packs, a list of relevant 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:

Data:

Syllabus

DateTopicCourse pack readingOnline resourcesNotes
Tuesday, Sept. 5IntroductionChapter 1Info sheet
Thursday, Sept. 7Technological and social networksChapters 2 and 3
Tuesday, Sept. 12Information networks and biological networksChapters 4 and 5Homework 1Homework 1 handed out
Thursday, Sept. 14Basic mathematics of networks6.1-6.10
Tuesday, Sept. 19Paths, components, and the graph Laplacian6.11-6.14Homework 2Homework 1 due, Homework 2 handed out
Thursday, Sept. 21Centrality7.1-7.2
Tuesday, Sept. 26Transitivity and assortativity7.3-7.7Homework 3, Data fileHomework 2 due, Homework 3 handed out
Thursday, Sept. 28Computer algorithms8.1-8.4
Tuesday, Oct. 3Paths and flows8.5-8.7Homework 4, Data fileHomework 3 due, Homework 4 handed out
Thursday, Oct. 5Statistics and errorsChapter 9
Tuesday Oct. 10Real-world network structure10.1-10.2Homework 4 due, no new homework this week
Thursday, Oct. 12Degree distributions and power laws10.3-10.7
Tuesday, Oct. 17No classFall Break
Thursday, Oct. 19Midterm 1
Tuesday, Oct. 24Random graphs 111.1-11.5Homework 5 handed out
Thursday, Oct. 26Random graphs 211.6-11.8
Tuesday, Oct. 31Configuration models 112.1-12.5Homework 5 due, Homework 6 handed out
Thursday, Nov. 2Configuration models 212.6-12.8
Tuesday, Nov. 7Configuration models 312.9-12.11Homework 5 due, Homework 6 handed out
Thursday, Nov. 9Generative models 113.1, 13.2
Tuesday, Nov. 14Generative models 213.3-13.6Homework 6 due, no new homework this week
Thursday, Nov. 16Midterm 2
Tuesday, Nov. 21Community structure 114.1-14.2Homework 7 handed out, due Dec. 5
Thursday, Nov. 23No classThanksgiving
Tuesday, Nov. 28Community structure 214.4-14.6
Thursday, Nov. 30Percolation15.1-15.5
Tuesday, Dec. 5Epidemics on networks16.1-16.3Homework 7 due
Thursday, Dec. 7Network searchChapter 18In class, usual time and place
Tuesday, Dec. 12Midterm 3In class, usual time and place

Mark Newman