### Provided by:

IMT

### Sede:

IMT Lucca

### Lecturers:

Guido CALDARELLI, T. SQUARTINI, G. CIMINI

### Semester:

2

### Hours:

40

### Exam:

Y

### Educational Goals:

The course aims at providing an overview of methods to analyse complex networks.

### Prerequisites:

Solid mathematical background, scientific curiosity, interest in multidisciplinarity, passion for theory.

### Programme:

Part I - Introduction to Complex Networks (Graph Theory Introduction. Properties of Complex Networks. Community Detection. Ranking Algorithms. Static Models of Graphs. Dynamical Models of Graphs. Fitness Models. Financial Networks).
Part II - Algorithms and Applications (Centrality Measures. Spectral Properties of Graphs. Community Detection. Bipartite Networks. Ranking and Reputation Algorithms. Trade Network Datasets. Multilayer Networks. Infrastructural Networks).
Part III - Statistical Mechanics of Networks (Complex Networks Randomization: A Primer. Basics of Information Theory. The Exponential Random Graphs Framework: From Zero to Shannon. The Maximum-Likelihood Recipe for Parameters Estimation. Hypothesis Testing on Networks: Pattern Detection, Network Filtering, Network Projection. The Dutch Interbank Network Case-Study. Network Reconstruction: A Survey of Existing Methods. Network Reconstruction: Moving Towards Entropy-Based Recipes. The World Trade Web Case-Study. International Economic Networks: The Interplay between Trade, Finance, Production and Migrations).
Part IV - Dynamical Processes on Networks (Master Equations, Models of Growing Networks - Continuous Description. Epidemics. Scaling and Percolation on Networks. Contagion in Financial Networks. Game Theory).