Description

The theory of complex networks provides generic tools to model and analyse systems in a broad range of disciplines, including biology, sociology, economics, physics and information science. Processes such as the dynamics of epidemics, the diffusion of information in social networks, the interactions between species in ecosystems, the evolution of urban systems or the communication between neurons in our brains are all actively studied using dynamical models on complex networks. In these systems, the patterns of connections between the systems' components at the local and mesoscopic levels play a fundamental role in the global dynamics. Studying these patterns allows one to better understand and predict the behaviour of these complex systems.

This module aims at providing an introduction to this interdisciplinary field of research by integrating tools from graph theory, statistics and dynamical systems. Applications related to current problems related to biological, urban and social systems as well as the impact of digitalisation on society will serve as examples during the lecture.

Resources

The slides of the course are available in the Download section.

The main resource for this course is the book "Networks" by Mark Newman accessible from the UZH network here: Newman, M. (2018). Networks 2nd ed. Oxford University Press or from anywhere in the world with the UZH VPN.

Other useful resources

Books:

• Lambiotte, R., & Schaub, M. T. (2021). Modularity and Dynamics on Complex Networks. Cambridge University Press.
• Latora, V., Nicosia, V., & Russo, G. (2017). Complex networks: principles, methods and applications. Cambridge University Press.
• Estrada, E. (2012). The structure of complex networks: theory and applications. Oxford University Press.
• Caldarelli, G., & Chessa, A. (2016). Data science and complex networks: real cases studies with Python. Oxford University Press.
• Menczer, F., Fortunato, S., & Davis, C. A. (2020). A first course in network science. Cambridge University Press.
• Pósfai, M., & Barabási, A. L. (2016). Network science. Cambridge University Press. (online)
• Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge university press.

General/Review articles about network science:

• Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268-276.
• Albert, R., & Barabasi, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47–97.
• Newman, M. E. J. (2003). The Structure and Function of Complex Networks. SIAM REVIEW, 45(2), 167–256.
• Boccaletti, S., S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4–5), 175–308.
• Butts, C. T. (2009). Revisiting the foundations of network analysis. Science, 325(5939), 414-416.
• Cimini, G., Squartini, T., Saracco, F., Garlaschelli, D., Gabrielli, A., & Caldarelli, G. (2018). The Statistical Physics of Real-World Networks. Nature Reviews Physics, 1 (January).

Online resources:

• Nice visualization and explanation of percolation on the grid: "Percolation: a Mathematical Phase Transition" https://youtu.be/a-767WnbaCQ?si=u7Di7gsVgjiE2L0S