The course is organized into four parts. The first two parts are devoted to the characterization of the structural properties of real world networks, and to the development of new network models. It contains topics of graph theory, social networks analysis, statistical physics, molecular biology, urban planning. Part three is on the study of different kinds of dynamical processes that take place over a network. Special emphasis is given to percolation processes and network tolerance to errors and external attacks, cascading failures in infrastructure networks, diffusion of infectious diseases in a population, dynamics of social groups, searching in the World Wide Web. Part four is on collective behaviors such as synchronization in networks of dynamical units. In each of the four parts, the theory is supplemented with examples and applications, databases of real world networks, and with numerical algorithms.

The course is organized in 10 lectures of 3 hours each, and 2 seminars.

• The importance of being central . P. Crucitti and V. Latora, Proc. 31st Workshop Erice, World Scientific (2005).
• Centrality measures in spatial networks of urban streets . P. Crucitti, V. Latora and S. Porta, Phys. Rev. E73, 036125 (2005)
• Interaction ruling animal collective behavior depends on topological rather than metric distance . M. Ballerini et al, PNAS 105, 1232 (2008)

• Notes: CAP2.PDF
• Complex networks: Structure and dynamics. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Physics Reports 424, 175 (2006).
• Physarum solver: A biologically inspired method of road-network navigation. A. Teroa, R. Kobayashia, T. Nakagaki, Physica A363, 115 (2006).

• Mean-field theory for scale-free random networks . A.L. Barabasi, R. Albert and H. Jeong, Physica A272, 173 (1999).
• Connectivity of Growing Random Networks . P. L. Krapivsky, S. Redner and F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000).
• Topology of Evolving Networks: Local Events and Universality. R. Albert and A.L. Barabasi, Phys. Rev. Lett. 85, 5234 (2000).
• Scale-free Nets from Varying Vertex Intrinsic Fitness . G. Caldarelli, A. Capocci, P. De Los Rios and M. A. Munoz, Phys. Rev. Lett. 89, 258702 (2002).

• Dynamical and Correlation Properties of the Internet . R. Pastor-Satorras, A. Vazquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
• Assortative Mixing in Networks M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2001).

• Attack and error tolerance of complex networks. R. Albert, H. Jeong, and A.L. Barabasi, Nature 406, 378 (2000).
• Resilience of the internet to random breakdowns . R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000).
• Breakdown of the internet under intentional attack. R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001).
• Percolation critical exponents in scale-free networks. R. Cohen, D. ben Avraham, and S. Havlin, Phys. Rev. E66, 36113 (2002).
• Percolation in directed scale-free networks . N. Schwartz, R. Cohen, D. ben Avraham, A.-L. Barabasi and S. Havlin, Phys. Rev. E66, 015104(R) (2002).
• Vulnerability and protection of critical infrastructures . V. Latora and M. Marchiori, Phys. Rev. E71, 015103(R) (2005)

• The web of human sexual contacts . F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y, Aberg, Nature 411, 907 (2001).
• Epidemic spreading in scale-free nets . R. Pastor-Satorras and A. Vespignani. Phys. Rev. Lett. 86, 3200 (2001).
• Epidemic dynamics and endemic states in complex nets . R. Pastor-Satorras and A. Vespignani. Phys. Rev. E63, 066117 (2001)
• Epidemic dynamics in finite size scale-free networks . R. Pastor-Satorras and A. Vespignani, Phys. Rev. E65, 035108(R) (2002)
• Immunization of complex networks . R. Pastor-Satorras and A. Vespignani, Phys. Rev. E65, 036104 (2002).
• Halting viruses in scale-free networks . Z. Dezso and A.L. Barabasi, Phys. Rev. E65, 055103(R) (2002).
• Infection dynamics on scale-free networks. R.M. May and A.L. Lloyd, Phys. Rev. E64, 66112, (2001).
• Epidemic outbreaks in complex heterogeneous networks. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B26, 521 (2002).
• Spread and epidemic disease on networks . M.E.J. Newman, Phys. Rev. E66, 016128 (2002).
• Spreading of sexually transmitted diseases in heterosexual populations . J. Gomez-Gardenes, V. Latora, Y. Moreno, E.V. Profumo, PNAS 105, 1399 (2008)

• Slides: Game theory
• Dynamical Organization of Cooperation in Complex Topologies . J. Gomez-Gardenes, M. Campillo, L. M. Floria, and Y. Moreno, PRL 98, 108103 (2007)
• Complex cooperative networks from evolutionary preferential attachment . J. Poncela, J. Gomez-Gardenes, M. Floria, A. Sanchez, Y. Moreno

• Slides: Sistemi che si sincronizzano
• Disease spreading in populations of moving agents . A. Buscarino, L. Fortuna, M. Frasca, V. Latora, arXiv:0707.1673
• Epcast: Controlled Dissemination in Human-based Wireless Networks by means of Epidemic Spreading Models S. Scellato, C. Mascolo, M. Musolesi, V. Latora, arXiv:0711.2780
• Synchronization of Metronomes J. Pantaleone, Am. J. of Phys 2002
• Synchronization of pulse-coupled Biological Oscillators Mirollo and S. Strogatz, SIAM J. Appl. Math 1990
• Synchronization of Moving Chaotic Agents M Frasca, A. Buscarino, A. Rizzo, L. Fortuna, S. Boccaletti, PRL 100, 044102 (2008)

• Slides: Modularity for community detection