Course syllabus

# NĂ¤tverksdynamik

Network Dynamics

## FRTN30, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Network Dynamics

Valid for: 2021/22

Faculty: Faculty of Engineering, LTH

Decided by: PLED F/Pi

Date of Decision: 2021-04-23

Elective for: C4, D4, E4-ra, F4, F4-fm, F4-r, I4-fir, Pi4, MMSR1

Language of instruction: The course will be given in English

Networks are ubiquitous in our modern society: infrastructure
networks, providing communication, transportation, energy services;
social networks, determining our information, influencing our
opinions, and shaping our political views; economic and financial
networks, determining the nature of economic interactions and
financial linkages; and natural networks (e.g., biological and
physical networks), governing the evolution and spread of natural
phenomena.

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 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 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 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

- 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.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam (5 hours), four homework assignments. In the case of less than 5 registered students, the retake exams may be given in oral form.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts

Code: 0115. Name: Examination.

Credits: 7,5. Grading scale: TH.

Code: 0215. Name: Homework Assignment 1.

Credits: 0. Grading scale: UG.

Code: 0315. Name: Homework Assignment 2.

Credits: 0. Grading scale: UG.

Code: 0415. Name: Homework Assignment 3.

Credits: 0. Grading scale: UG.

Code: 0515. Name: Homework Assignment 4.

Credits: 0. Grading scale: UG.

Assumed prior knowledge: Basic knowledge within mathematics, mathematical statistics, and linear dynamical systems, including Linear Algebra, Multidimensional Analysis, Mathematical Statistics, Basic Course, and Linear Analysis or Automatic Control, Basic Course.

The number of participants is limited to: No

- 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. Online available at 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.

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

Director of studies: Anton Cervin, anton.cervin@control.lth.se

Course homepage: http://www.control.lth.se/course/FRTN30