Part I (16 hours)
THEORY
L1. Basic Definitions, Statistical Distributions, Universality, Fractals, Self-Organised Criticality
a. L. A. Adamic Zipf, Power-laws and Pareto - a ranking tutorial (2002)
b. Bak, P., Tang, C. & Wiesenfeld, K. Phys. Rev. Lett. 59, 381–384 (1987).
c. Mitzenmacher, M. A Internet Math. 1, 226–251 (2004).
L2. Properties of Complex Networks, scale invariance of degree, small world, clustering, modularity
a. M.E.J. Newman SIAM Review (2003)
b. R. Albert, A.-L Barabási Review of Modern Physics 74, 47 (2001)
L3. Handling Graphs Pajek, Python, format of available software and visualization and plotting
a. http://vlado.fmf.uni-lj.si/pub/networks/pajek
b. G. Caldarelli, A. Chessa Data Science and Complex Networks OUP (2016).
L4. Basic on centrality and communities, closeness, betweenness, modularity
a. L. Katz Psychometrika 18, 39–43 (1953).
L5. Different kinds of networks, hypergraphs, multigraphs. simplicial complexes
a. G. Ghoshal, V. Zlatić, G. Caldarelli, M.E.J. Newman, Phys Rev E 79, 066118 (2009).
b. V. Zlatić, G. Ghoshal, G. Caldarelli, Phys Rev E 80, 036118 (2009).
c. Bianconi, G. Multilayer Networks. Multilayer Networks: Structure and Function, OUP (2018).
L6. Ranking in Graphs
a. Page, L., Brin, S., Motwami, R., Winograd, T. & Motwani, R. (Stanford InfoLab, 1999).
b. Kleinberg, J. ACM Comput. Surv. 31, 5-es (1999).
L7. Static Models Random Graph, Small World, configuration models
a. Erdös, P. & Rényi, A. Publ. Math. Debrecen 6, 290–297 (1959).
b. Watts, D. J. & Strogatz, S. H. Nature 393, 440–442 (1998).
L8-L9. Dynamic Models Barabási-Albert and modifications
a. R. Albert, A.-L Barabási Review of Modern Physics 74, 47 (2001)
L10. Fitness models
a. Bianconi, G. & Barabási, A.-L. Europhys. Lett. 54, 436–442 (2001).
b. G. Caldarelli, A. Capocci, P. De Los Rios, M.A. Muñoz, Phys Rev Lett 89, 258702 (2002).

APPLICATIONS
L11. Networks in Medicine I Molecular Networks
Invited talk and discussion Prof. Paola Paci (Univ. Sapienza Roma)
L12. Networks in Medicine II Molecular Networks and COVID related research
Invited talk and discussion Prof. Paola Paci (Univ. Sapienza Roma)
L13. Ecological Networks I Definition of Food Chain, food webs 
Invited talk and discussion Dr. Samir Suweis (Univ. Padova)
L14. Ecological Networks II Examples
Invited talk and discussion Dr. Samir Suweis (Univ. Padova)
L15. Brain Networks I Detection Tools, fMRI
 Invited talk and discussion Dr. Tommaso Gili (IMT Lucca)
L16. Brain Networks II Network based tools for diagnosis
 Invited talk and discussion Dr. Tommaso Gili (IMT Lucca)
a. R. Mastrandrea, F. Piras, A. Gabrielli, G. Caldarelli, G. Spalletta, T. Gili arXiv:1901.08521

 
PART II (14 hours)
THEORY
L17 L18 L19 L20 Python Course
Invited talk and discussion with Dr. Fabio Saracco (IMT Lucca)
L21. Trees and River Networks
a. Maritan, A. et al. Scaling laws for river networks. Phys. Rev. E 53, 1510–1515 (1996).
L22 Laplacian Graphs
L23 L24. Financial Networks Debtrank, Pathways to Complexity
a. Battiston, S. et al. DebtRank: too central to fail? Financial networks, the FED and systemic risk. Sci. Rep. 2, 541 (2012).
b. M. Bardoscia,  S. Battiston, F. Caccioli,  G. Caldarelli, Nature Communications 8 14416 (2017)

APPLICATIONS
L25. Banks
G. De Masi, G. Iori. G. Caldarelli, Physical Review E 74, 066112 (2006).
L26 Economic Networks World Trade Web, Economic Complexity
a. Hidalgo, C. A. et al. Science 317, 482–487 (2007).
L27. Fake News, definition Twitter, Facebook WWW
L28. Fake News bots
a. Caldarelli, G., De Nicola, R., Del Vigna, F., Petrocchi, M. & Saracco, F. . Commun. Phys. 3, 81 (2020)
L29. Epidemics Dynamical Processes on Networks
a. Pastor-Satorras, R. & Vespignani, A., Phys Rev Lett 86, 3200–3203 (2001).
L30 Epidemic Models SI, SIR, models for COVID-19