Course Syllabus for

Network Dynamics

FRTN30F, 7.5 credits

Valid from: Spring 2017
Decided by: Professor Thomas Johansson
Date of establishment: 2016-10-27

General Information

Division: Automatic Control
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FRTN30
Teaching language: English


The course provides 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

D. Easley & J. Kleinberg: Networks, crowds and markets, reasoning about a highly connected world. Cambridge University Press, 2010, ISBN: 978-0-521-19533-1. Supplement to lecturer's notes. R. Van Der Hofstad: Random Graphs and Complex Networks. Supplement to lecturer's notes. Tillgänglig online via D. Levin, Y. Peres, E. Wilmer: Markov chains and mixing times. American Mathematical Society, 2009, ISBN: 978-0-8218-4739-8. Supplement to lecturer's notes.

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination formats: Written exam, written assignments. Skriftlig examen, fyra godkända inlämningsuppgifter.
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FRT010 Automatic Control, Basic Course

Course Occasion Information

Contact and Other Information

Course coordinator: Giacomo Como <>

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