Course Syllabus for

# Network Dynamics Nätverksdynamik

## 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

## Aim

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.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• know the basic principles of graph theory and apply them to model real-world networks
• have insight in the basic differences between different models of random graphs
• be familiar with the properties of random walks on graphs
• be able to analyze simple dynamical systems over networks
• understand emerging phenomena in large-scale networks
• be able to give an overview of modern directions in network science

Competences and Skills

For a passing grade the doctoral student must

• be able to analyze properties of (random) graphs both quantitatively and qualitatively
• be able to handle basic analytical computations for random walks
• be able to analyze simple dynamical systems over networks and to relate their behavior to the network structure
• be able to use computer tools for simulation and analysis of networks

Judgement and Approach

For a passing grade the doctoral student must

• be able to understand relations and limitations when simple models are used to describe complex networks
• be able to evaluate dominating emerging phenomena in network dynamics

## 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 http://www.win.tue.nl/~rhofstad/. 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
Examiner:

## Admission Details

Assumed prior knowledge: FRT010 Automatic Control, Basic Course

## Contact and Other Information

Course coordinator: Giacomo Como <giacomo.como@control.lth.se>