Course syllabus

Nätverksdynamik
Network Dynamics

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

Valid for: 2014/15
Decided by: Education Board B
Date of Decision: 2014-04-08

General Information

Elective for: D4, E4-ra, F4, F4-r, Pi4-bg
Language of instruction: The course will be given in English

Aim

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 focus on common mathematical principles that permeate the structure and functioning of these networks. It will introduce conceptual tools from dynamical systems, (random) graph theory, Markov chains, optimization and game theory. It will also cover a variety of applications including: learning and informational cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; control of transportation and energy networks.

Learning outcomes

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
• show ability for teamwork and collaboration in groups.

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.

Examination details

Grading scale: TH
Assessment: Written exam (5 hours), four homework assignments. When less then five registered the exam may be oral.

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.

Admission

Required prior knowledge: FRT010 Automatic Control, Basic Course.
The number of participants is limited to: No

Reading list

• 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.

Contact and other information

Course coordinator: Giacomo Como, giacomo.como@control.lth.se
Director of studies: Karl-Erik Årzén, karlerik@control.lth.se