After successful completion of the course, students are able to...

• Explain basic concepts of network science
• Apply these methods to financial markets
• Do their own analysis of the financial network, and identify the most important properties of the market
• Identify the riskiest elements of financial networks and learn ways how to manage the risk

• Networks – definitions, basic concepts (node, link, degree, adjacency matrix)
• Basic types of networks (undirected, directed, weighted, bipartite, multiplex)
• Node degree (distribution, in-degree, and out-degree, nearest-neighbor degree, assortativity)
• Centrality measures (degree, closeness, betweenness, eigenvector, Katz, clustering coefficient, Pagerank)
• Random network models (Erdös-Rényi network, percolation transition, Wigner law)
• Complex network models (Configuration model, small-world networks, Strogratz-Watts model, scale-free network, Albert-Barabási model)
• Community detection algorithms (Betweenness, Modularity, Infomap, Louvain, Leiden, Hierarchical clustering)
• Correlation networks (eigenvector decomposition, random and non-random modes)
• Network filtering algorithms (minimum spanning tree, planar maximally filtered graph)
• Information-theoretic measures (entropy, mutual information, transfer entropy)
• Financial networks analysis (in R project)
• Multilayer financial networks (DebtRank, risk management)
• Basic types of networks (undirected, directed, weighted, bipartite, multiplex)
• Node degree (distribution, in-degree, and out-degree, nearest-neighbor degree, assortativity)
• Centrality measures (degree, closeness, betweenness, eigenvector, Katz, clustering coefficient, Pagerank)
• Random network models (Erdös-Rényi network, percolation transition, Wigner law)
• Complex network models (Configuration model, small-world networks, Strogratz-Watts model, scale-free network, Albert-Barabási model)
• Community detection algorithms (Betweenness, Modularity, Infomap, Louvain, Leiden, Hierarchical clustering)
• Correlation networks (eigenvector decomposition, random and non-random modes)
• Network filtering algorithms (minimum spanning tree, planar maximally filtered graph)
• Information-theoretic measures (entropy, mutual information, transfer entropy)
• Financial networks analysis (in R project)
• Multilayer financial networks (DebtRank, risk management)

lecture and exercises/homework

exercises/homework and oral exam

• S. Thurner, R. Hanel, P. Klimek, Introduction to the Theory of Complex Systems (Oxford University Press 2018, ISBN: 978-0198821939).
• M. Newman, Networks: An Introduction (Oxford University Press 2010, ISBN: 978-0199206650).
• K. Soramäki, S. Cook, Network Theory and Financial Risk (Risk, 2022, ISBN: 978-1-78272-432-2).
• M. Bardoscia et al., The physics of financial networks, Nature Reviews Physics 3, p. 490–507 (2021). DOI: 10.1038/s42254-021-00322-5.