THEORY AND APPLICATION OF COMPLEX NETWORKS

The aim of the course is to provide the student with a general overview of Graph Theory and models of complex networks. Such theoretical basis will be used to understand and describe a variety of real world systems. Relevance of data collected will be analysed with statistical methods based on Information theory and Statistical Physics. To this purpose, various multidisciplinary applications are presented. Most of them are of direct interest for the course of study. But also those that seem more general are interesting for students since they show the correct way to apply the theoretical tools defined in the first part of course(s). Students will be exposed to these topics at a PhD level, with a special emphasis on the state of the art.
A preliminary version of the slides can be downloaded from http://www.guidocaldarelli.com/index.php/phd-lectures

At the end of the course, students are expected to be able to read the current literature in this area, identify the optimal technique (experimental, theoretical or computational), and tackle a specific problem, by collecting and analyzing the data and modeling the phenomenon

Fundamental tools of Mathematics and Physics, calculus, linear algebra, probability distributions, entropy

Part I (15 hours)
THEORY
<b>L1. Basic Definitions, Statistical Distributions, Universality, Fractals, Self-Organised Criticality</b>
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 (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, PRE 79 066118 (2009).
b. V. Zlatić, G. Ghoshal, G. Caldarelli, PRE 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. Dynamic Models Barabási-Albert and modifications
a. R. Albert, A.-L Barabási Review of Modern Physics (2001)
L9. 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, PRL 89, 258702 (2002).
APPLICATIONS
L10. Networks in Medicine I, Diseasome
L11. Networks in Medicine II Molecular Networks
L12. Ecological Networks I Definition of Food Chain, food webs
L13. Ecological Networks II Examples
L14. Brain Networks I Detection Tools, fMRI
L15. Brain Networks II Network based tools for diagnosis
a. R. Mastrandrea, F. Piras, A. Gabrielli, G. Caldarelli, G. Spalletta, T. Gili arXiv:1901.08521

PART II (15 hours)
THEORY
L16. River Networks, Trees
a. Maritan, A. et al. Scaling laws for river networks. Phys. Rev. E 53, 1510–1515 (1996).
L17. Bipartite Networks
L18. Spectral Properties Eigenvectors Eigenvalues,
L19. Laplacian Graphs
L20. Statistical Physics of Networks I, Information Theory, entropy, Maximum Likelihood
a. Bianconi, G. PRE 79, 036114 (2009)
L21. Statistical Physics of Networks II Reconstruction and Relevance
a. G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli Nature Physics Reviews 1, 52-70 (2019).
L22. Centrality Measures
L23. Epidemics Dynamical Processes on Networks
a. Pastor-Satorras, R. & Vespignani, A., PRL 86, 3200–3203 (2001).
L24. Epidemic Models SI, SIR, models for COVID-19
APPLICATIONS
L25. Social Networks I, Computational Social Science, historical networks
L26. Social Networks II, historical networks
L27. Economic Networks World Trade Web, Economic Complexity
a. Hidalgo, C. A. et al. Science 317, 482–487 (2007).
L28. Financial Networks Debtrank
a. Battiston, S. et al. DebtRank: too central to fail? Financial networks, the FED and systemic risk. Sci. Rep. 2, 541 (2012).
L29. Fake News, definition Twitter, Facebook WWW
L30. Fake News bots
a. Caldarelli, G., De Nicola, R., Del Vigna, F., Petrocchi, M. & Saracco, F. . Commun. Phys. 3, 81 (2020)

• G. Caldarelli Scale-Free Networks OUP (2007)
• Easley, Kleinberg “Networks Crowds and Markets” CUP (2010)
http://www.cs.cornell.edu/home/kleinber/networks-book/
• A-L Barabási Network Science CUP (2016) http://networksciencebook.com/

The final exam will be based on a report and a presentation by the students on a specific topic agreed with the instructor

Traditional interacting methods, on-line teaching, or a combination of the two will be used, depending on students logistic and situations

oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development