Structure and Dynamics of Networks

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Extract information about stochastic processes, such as the probability distribution and critical phenomena.
• Express stochastic processes mathematically as dynamical equations on networks for the probability of stochastic outcomes.
• Explain real world phenomena in complex dynamical networks, such as synchronisation and scale-free network structures
• Investigate a topic related to networks and present your results.
• Explain the relation between some network structural and spectral properties, and their significance for real-world networks
• Define basic network properties, compute them in theoretical and practical situations, and explain their significance in network modelling
• Utilise graph theoretical tools to determine the stability of complex dynamical systems

Part I: Network structure and eigenvalues

• Network terminology
• Network eigenvalues and eigenvectors, and their relation to structural network properties

Part II: Dynamics of and on networks

• Dynamics on complex networks: stability and asymptotic trajectories
• Examples of dynamical processes on and of networks: models of coupled oscillators, growing (scale-free) networks

Part III: Stochastic dynamics on networks

• Introduction to stochastic processes and how they related to dynamical systems on networks
• Discussion of particular real world stochastic systems: random walks, gene regulatory networks, epidemics

Lectures, tutorials, guided reading and private study. The lectures will be based on selected material from the reading list. Lectures will give an overview of the topic and introduce the main references and students are expected to demonstrate in-depth independent learning through private study. The module is organised in three blocks of four weeks each.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.