Networks are universal understructures of the real world. In this course, starting with elementary facts on the network (graph) theory, typical generative models of networks, characterization of networks by the spectrum and other statistical quantities, and dynamical processes on networks are explained.
The aim of this course is to learn the elements of network (graph) theory and to understand how to mathematically model and analyze real-world complex networks.
Networks (graphs), spectrum, random walks, diffusion, dynamics
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
lectures, homework
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction | Learn examples of networks and elementary mathematical models |
Class 2 | Generative models of networks | Understand representative generative models of networks |
Class 3 | Statistical quantities and spectrum | Understand typical statistical quantities and Laplacian spectrum of networks |
Class 4 | Robustness of networks | Understand the notion of network robustness |
Class 5 | Random walks and diffusion | Understand random walks and diffusion on networks |
Class 6 | Epidemic models | Understand representative epidemic models on networks |
Class 7 | Coupled oscillator networks | Understand dynamics of coupled oscillators on networks |
Class 8 | Self-organization on networks | Understand pattern formation on networks |
Dorogovtsev, "Lectures on complex networks", Oxford
Barrat, Barthelemy, Vespignani, "Dynamical Processes on Complex Networks", Cambridge.
Grading will be based on homework scores.
Elementary knowledge of mathematics and physics