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.

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.

- 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)

- Physics preprints
*Pajek*network software for Windows (also runs on Linux or Mac using Wine or SoftPC)*GraphViz*network software for any platform (Windows, Linux, Mac)*Yed*network software for any platform (Windows, Linux, Mac)

- Homework 1 - Fundamental mathematics of networks
- Homework 2 - Centrality measures
- Homework 3 - Degree distributions, clustering, etc.
- Homework 4 - Computer algorithms
- Homework 5 - Random graphs
- Homework 6 - The configuration model
- Homework 7 - Configuration models and growing networks
- Homework 8 - Growing networks and the small-world model
- Homework 9 - Percolation and epidemics

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

Tuesday, Sept. 8 | Introduction | Chapter 1 | Information sheet | |

Thursday, Sept. 10 | Technological and social networks | Chapters 2 and 3 | ||

Tuesday, Sept. 15 | Information and biological networks | Chapters 4 and 5 | ||

Thursday, Sept. 17 | Mathematics of networks | 6.1-6.11 | Homework 1 | Homework 1 handed out |

Tuesday, Sept. 22 | Centrality | 7.1-7.7 | ||

Thursday, Sept. 24 | Transitivity, reciprocity, etc. | 7.8-7.13 | Homework 2 | Homework 2 handed out |

Tuesday, Sept. 29 | Observed structure of networks | Chapter 8 | ||

Thursday, Oct. 1 | Data structures and complexity | Chapter 9 | Homework 3 | Homework 3 handed out |

Tuesday, Oct. 6 | Shortest paths | 10.1-10.5 | ||

Thursday, Oct. 8 | Maximum flows and minimum cuts | 6.12 and 10.6 | Homework 4 | Homework 4 handed out |

Tuesday, Oct. 13 | Matrix algorithms | 11.1-11.3 | ||

Thursday, Oct. 15 | Graph partitioning | 11.4-11.11 | No homework this week | |

Tuesday, Oct. 20 | No class | Fall Break | ||

Thursday, Oct. 22 | Mid-term exam | Practice problems, solutions | In-class, usual time and place | |

Tuesday, Oct. 27 | Random graphs 1 | 12.1-12.5 | ||

Thursday, Oct. 29 | Random graphs 2 | 12.6-12.8 | Homework 5 | Homework 5 handed out |

Tuesday, Nov. 3 | Configuration models 1 | 13.1-13.4 | ||

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

Tuesday, Nov. 10 | Configuration models 3 | 13.9-13.11 | ||

Thursday, Nov. 12 | Generative models 1 | 14.1-14.2 | Homework 7 | Homework 7 handed out |

Tuesday, Nov. 17 | Generative models 2 | 14.3 | ||

Thursday, Nov. 19 | Generative models 3 | 14.4-14.5 | Homework 8 | Homework 8 handed out, due Dec. 3 |

Tuesday, Nov. 24 | The small-world model | 15.1 | ||

Thursday, Nov. 26 | No class
| Thanksgiving | ||

Tuesday, Dec. 1 | Percolation | Chapter 16 | ||

Thursday, Dec. 3 | Epidemics on networks | 17.1-17.8 | Homework 9 | Homework 9 handed out |

Tuesday, Dec. 8 | Network search | Chapter 19 | ||

Thursday, Dec. 10 | Review | Review topics, Sample problems | Last class | |

Monday, Dec. 21 | Final Exam |

Mark Newman