English

Varje vårtermin

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.

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.

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

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

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

Föreläsningar

Laborationer

övningar

Skriftlig tentamen

Inlämningsuppgifter

Skriftlig examen, fyra godkända inlämningsuppgifter.

Underkänd, godkänd

FRT010 Automatic Control, Basic Course

 

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.

FRTN30F

 -10-27

Professor Thomas Johansson