Course Syllabus for

Network Dynamics

FRT095F, 9 credits

Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-02-07

General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English


This course will provide an introduction to and some analysis of the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Motivation and applications will be drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must

Course Contents

Basic graph theory: connectivity, degree distributions, trees, adjacency matrices, spectrum. Random graphs: Erdos-Renyi, configuration model, preferential attachment, small-world, branching process approximations Flows and games on graphs: max-flow min-cut, optimal transport, Wardrop equilibria, evolutionary dynamics. Random walks on graphs: invariant distributions, hitting times, mixing times. Dynamical systems on graphs: distributed averaging, interacting particle systems, epidemics, opinion dynamics. Mean-field and branching process approximations.

Course Literature

Lecture notes

Instruction Details

Types of instruction: Lectures, seminars, exercises, project

Examination Details

Examination formats: Written assignments, seminars given by participants
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: The course is designed for an audience of doctoral students with some mathematical background (in particular, probability and linear algebra at an intermediate level), possibly from the programs in Automatic Control, Mathematics, Mathematical Statistics, Physics, Computer Science, Economics, ...

Course Occasion Information

Contact and Other Information

Course coordinators:

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