| 1 | Introduction to Graph Theory: What is a graph? Basic concepts. Connectivity (connected components, reachability, biconnected components, spanning trees, bipartite graphs) | Gianluca Della Vedova
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| 2 | Walks, Paths, Trials, Cycles (Hamiltonian cycles, Eulerian cycles, TSP) | Marco Viviani |
| 3 | Graph matching (perfect matching, algorithm on bipartite graphs) | Gianluca Della Vedova |
| 4 | Graph decomposition (Modular decomposition, cographs) | Gianluca Della Vedova |
| 5 | Graph coloring (perfect graphs). Treewidth, pathwidth, Twin-width. | Gianluca Della Vedova |
| 6 | Graph compression
| Marco Viviani |
| 7 | Graph embedding
| Mauricio Soto |
| 8 | Graph mining (first part) | Marco Viviani |
| 9 | Graph mining (second part) | Marco Viviani |
| 10 | Graph partitioning (and clustering) & complex networks (graphs to represent complex systems and networks, small-world). | Marco Viviani |
