Overview:
Network structures are pervasive in the world
around us, from the Internet and the power grid, to social acquaintance networks,
to biological networks. This course is intended for graduate students interested in
learning about modern perspectives on networks, and should allow students to incorporate
network theory into their own research. This course will cover General Techniques and Selected Applications.
Prerequisites:
Familiarity with: linear algebra, basic statistics, calculus, ordinary
differential equations, using computer software.
Course structure: (1) Lectures, (2) bi-weekly problem sets/paper reviews, and (3) a class project or deeper HW assignments.
(i.e., Everyone does (1) and (2), then for (3) it is either a project or more technical homeworks.)
Topics: This course assumes no prior knowledge of networks. We will begin with basic concepts about networks and the mathematical tools for their analysis, developing key metrics for characterizing the structure of a network. We will then examine several models of network growth (random graphs, preferential attachment, small-worlds). Emphasis will then shift to network function and algorithms, such as the Page Rank algorithm for ranking web pages, and also decentralized search and routing in social and information networks. The next topics to be covered will reflect student interest.
Paper reviews: For these assignments, you are required to provide a short summary (one or two paragraphs) and a review of the strengths and weaknesses of the paper. The goal of these reviews is to help you synthetize the main ideas and concepts presented in each paper. Note, not all students will review the same papers. Based on your interests, you will choose the papers.
Project: Students work in small groups of 5-6 students on a course project. The projects will complement and extend the lecture material. The project may include simulation and modeling, network visualization, creating software for network analysis, or analysis of a real-world network (such as a transportation, social, biological or ecological network). We will be posting a list of potential project topics.
Resources:
There will be no required text for this course. The content will largely come from articles and class notes.
Important References. The class will draw from:
Basics of networks
Network Science Book, by A.-L. Barabasi (with M. Martino and M. Posfai).
Networks: An Introduction, 2nd Edition, by M. E. J. Newman, Oxford University Press, 2018.
The Structure and Function of Complex Networks, by
M. E. J. Newman, SIAM Review 45 (2), 167-256, 2003.
Dynamical processes on networks
Dynamical Processes on Complex Networks, Barrat, Barthelemy, Vespignani, Cambridge Univesity Press, 2008.
Dynamical Systems on Networks: A Tutorial, M. Porter and J. Gleeson, Springer 2016. (See also the arXiv version.)
Probability and random graphs
Random Graph Dynamics, by Rick Durrett, Cambridge Univesity Press, 2007.
Hofstad's course: Random Graphs and Complex Networks
pdf notes at: http://www.win.tue.nl/~rhofstad/NotesRGCN2013.pdf
Social and Economic networks
Social and Economic Networks, Matthew Jackson, Princeton University Press, 2008.
Networks, Crowds, and Markets: Reasoning About a Highly Connected World, D. Easley, J. Kleinberg, Cambridge University Press, 2010.
Looking for network data? Try:
ICON, the Colorado Index of Complex Networks
Barabasi book data sets
Related classes elsewhere:
Univ of Michigan, Mark Newman, Complex Systems 535, Fall 2017
Northeastern, Laszlo Barabasi's course, Fall 2017
Stanford, Matthew Jackson's course
Matthew Jackson's Books, MOOCs, etc
Univ of Michigan, Lada Adamic, Intro to networks, Fall 2009
Cornell, Networks Journal Club
U Nevada at Reno, CS 765, Spring 2013
Hofstad's course: Random Graphs and Complex Networks, 2013
Numerous Coursera classes
