Room: 455 Dennison

Instructor: Mark Newman

Office: 322 West Hall

Office hours: Wednesdays 1:30-3:30pm

Email: mejn@umich.edu

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.

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 in class on Thursday, October 21; the final will be on Friday, December 17 from 1:30pm till 3:30pm. Grade will be 35% on the homeworks, 30% on the mid-term, and 35% on the final.

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).

**Other books:** A list of other 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.

- R. K. Ahuja, T. L. Magnanti, and J. B. Orlin,
*Network Flows: Theory, Algorithms, and Applications*, Prentice Hall, Upper Saddle River, NJ (1993) - A. Barrat, M. BarthÃ©lemy, and A. Vespignani,
*Dynamical Processes on Complex Networks*, Cambridge University Press, Cambridge (2008) - S. N. Dorogovtsev and J. F. F. Mendes,
*Evolution of Networks*, Oxford University Press, Oxford (2003) - A. Degenne and M. Forse,
*Introducing Social Networks*, Sage, London (1999) - F. Harary,
*Graph Theory*, Perseus, Cambridge, MA (1995) - M. O. Jackson,
*Social and Economic Networks*, Princeton University Press, Princeton, NJ (2008) - C. D. Meyer,
*Matrix Analysis and Applied Linear Algebra*, SIAM, Philadelphia, PA (2000) - J. Scott,
*Social Network Analysis: A Handbook*, 2nd edition, Sage, London (2000) - S. Wasserman and K. Faust,
*Social Network Analysis*, Cambridge University Press, Cambridge (1994) - D. J. Watts,
*Six Degrees: The Science of a Connected Age*, Norton, New York (2003) - D. B. West,
*Introduction to Graph Theory*, Prentice Hall, Upper Saddle River, NJ (1996) - R. J. Wilson,
*Introduction to Graph Theory*, 4th edition, Addison-Wesley, Reading, MA (1997)

- Homework 1 - Fundamental mathematics of networks
- Homework 2 - Centrality
- Homework 3 - Degree distributions, paths, etc.
- Homework 4 - Algorithms
- Homework 5 - Random graphs
- Homework 6 - The configuration model
- Homework 7 - Generating functions and growing networks
- Homework 8 - Growing networks and the small-world model
- Homework 9 - Percolation and epidemics

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

Date | Topic | Reading | On-line resources | Notes |
---|---|---|---|---|

Tuesday, Sept. 7 | Introduction | Chapter 1 | ||

Thursday, Sept. 9 | Technological and social networks | Chapters 2 and 3 | ||

Tuesday, Sept. 14 | Information and biological networks | Chapters 4 and 5 | ||

Thursday, Sept. 16 | Mathematics of networks | 6.1-6.11 | Homework 1 | Homework 1 handed out |

Tuesday, Sept. 21 | Centrality | 7.1-7.7 | ||

Thursday, Sept. 23 | Transitivity, reciprocity, etc. | 7.8-7.13 | Homework 2 | Homework 1 due, Homework 2 handed out |

Tuesday, Sept. 28 | Component structure and the small-world effect | 8.1-8.2 | ||

Thursday, Sept. 30 | Degree distributions | 8.3-8.6 | Homework 3 | Homework 2 due, Homework 3 handed out |

Tuesday, Oct. 5 | Data structures and complexity | Chapter 9 | ||

Thursday, Oct. 7 | Shortest paths | 10.1-10.5 | Homework 4 | Homework 3 due, Homework 4 handed out |

Tuesday, Oct. 12 | Maximum flows and minimum cuts | 6.12 and 10.6 | ||

Thursday, Oct. 14 | Matrix algorithms and graph partitioning | Chapter 11 | Homework 4 due, no new homework this week | |

Tuesday, Oct. 19 | No class | Fall Break | ||

Thursday, Oct. 21 | Mid-term exam | Practice problems, solutions | In-class, usual time and place | |

Tuesday, Oct. 26 | Random graphs 1 | 12.1-12.5 | ||

Thursday, Oct. 28 | Random graphs 2 | 12.6-12.8 | Homework 5 | Homework 5 handed out |

Tuesday, Nov. 2 | Configuration models 1 | 13.1-13.4 | ||

Thursday, Nov. 4 | Configuration models 2 | 13.5-13.8 | Homework 6 | Homework 5 due, Homework 6 handed out |

Tuesday, Nov. 9 | Configuration models 3 | 13.9-13.11 | ||

Thursday, Nov. 11 | Generative models 1 | 14.1-14.2 | Homework 7 | Homework 6 due, Homework 7 handed out |

Tuesday, Nov. 16 | Generative models 2 | 14.3 | ||

Thursday, Nov. 18 | Generative models 3 | 14.4-14.5 | Homework 8 | Homework 7 due, Homework 8 handed out, due Dec. 2 |

Tuesday, Nov. 23 | The small-world model | 15.1 | ||

Thursday, Nov. 25 | No class
| Thanksgiving | ||

Tuesday, Nov. 30 | Percolation | Chapter 16 | ||

Thursday, Dec. 2 | Epidemics on networks | 17.1-17.8 | Homework 9 | Homework 8 due, Homework 9 handed out |

Tuesday, Dec. 7 | Network search | Chapter 19 | ||

Thursday, Dec. 9 | Review | Homework 9 due | ||

Friday, Dec. 17 | Final Exam |

Mark Newman