###### Collegio Carlo Alberto – MADAS

**15 hours lecture**

- 5/10/2018: 9h-11h
- 24/10/2018: 9h-11h, 11h-13h
- 7/11/2018: 9h-11h, 14h-16h
- 14/12/2018: 9h-11h, 11h-14h

###### Lecturer:

**Márton KARSAI** – marton.karsai@ens-lyon.fr

Office: ENS Lyon, IXXI, site Monod, N222

Tel: +33 426 233 805

Web: perso.ens-lyon.fr/marton.karsai

###### Materials:

The course consists of two parts. The first part is concentrating on the related theories, algorithms, models and measures of networks, while the second part gives an introduction to the different types, representations, and applications of complex networks.

Prerequisites: Background in graph theory, statistical analysis, and computer algorithms is an advantage but is not mandatory, as the course intends to be accessible for students coming from different disciplines

Evaluation: Attendants will need to pass a written exam in the end of the course.

When: October 2018 – January 2019

###### Subjects:

**Introduction and general network characteristics**- Complex systems as complex networks
- Representation of complex networks
- Characteristic measures of complex networks

**Models of complex networks**- Erdös-Rényi network model
- Configuration model
- Small-world networks, Watt-Strogatz model
- Scale-free networks, Barabási-Albert model

**Motifs and communities**- Motifs in static networks
- Communities – basics
- Modularity based methods: Girvan Newman algorithm, Louvain algorithm
- Overlapping communities: Link-communities, Clique percolation
- The Infomap method
- Network benchmarks

**Spreading processes on networks**- The Susceptible-Infected model process
- The Susceptible-Infected-Recovered model process
- Early and late time behaviour on scale-free networks
- Immunisation strategies

**Temporal networks**- Time-scales and representation
- Micro- and macroscopic measures of temporal networks
- Correlations in temporal networks
- Random reference models of temporal networks
- Generative models of temporal networks

**Multilayer and multiplex networks**- Definition and representation
- Characterization and general measures
- Interdependent networks
- Cascading failures in interdependent networks

**From data to networks**- Network construction from data
- Statistical analysis and fitting methods
- Sampling and biases
- Visualization and applications

###### Books:

- M.E.J. Newman, Networks, an Introduction (Oxford University Press)
- D. Easley, J. Kleinberg, Networks, Crowds, and Markets (Cambridge University Press)

###### Reviews:

- M.E.J. Newman, The structure and function of complex networks, SIAM Review 45, 167-256 (2003).R. Albert, A-L. Barabási, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74, 47-97 (2002)