Mathematics of Network Science

  • Instructor: Gergely Odor
  • Contact: odorgergo at gmail dot com
  • Prerequisites: Some familiarity with the basic concepts of calculus, probability theory, and linear algebra is assumed, but the most important concepts will be reviewed. Programming experience is useful; otherwise, the willingness to acquire some basic programming skills in Python is necessary to complete the practical sessions.
  • Text: The course is based on Grossglauser, Matthias, and Patrick Thiran. "Networks out of control: Models and methods for random networks." and class notes, which will be provided privately to the students. Additional reading is available here and here.

Course description:

The aim of the course is to get acquainted with the mathematical foundations of network science including elements of classical graph theory, random graph theory, and random processes on networks. Some applications from biology, sociology, economics, and other fields will be discussed.

The course will be provided in two hours of lectures, followed by two hours of practical sessions twice a week. The lectures will be focused on theory, while the practical sessions will focus on programming tutorials and programming assignments, which are intended to be solved and handed in at the end of the session. There will be 6 pen-and-paper homework assignments and one quiz (midterm exam). At the end of the term, students are expected to select a paper from a list provided by the instructor, and give a short 15 minute presentation about it.

Topics covered:

  • Introduction
  • Erdôs-Rényi graphs
  • Random walks on networks
  • Clustering
  • Stochastic Block model
  • Barabasi-Albert model
  • Configuration model
  • Watts-Strogatz model and Kleinberg model
  • Epidemics

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